types of polynomials 3x5y2 i - home | sardis secondary …sss.sd33.bc.ca/sites/default/files/unit 2...
TRANSCRIPT
![Page 1: Types of polynomials 3x5y2 I - Home | Sardis Secondary …sss.sd33.bc.ca/sites/default/files/Unit 2 Lessons Master.pdfFMPCIO Unit 2: Polynomials Lesson 1: Multiplying & Dividing Monomials](https://reader031.vdocument.in/reader031/viewer/2022012315/5ac158ed7f8b9a433f8cbd8b/html5/thumbnails/1.jpg)
FMPCIOUnit 2: Polynomials
Lesson 1: Multiplying & Dividing Monomials
3x5y2This is a term of a polynomial. The 3 is called the coefficIent, the x and y are calledthe variables, and the 5 and 2 are the exponents. The exponents must be wholenumbers.
Types of polynomials
# of Terms Example Type of Polynomial
I
2
3
4
DEGREE OF POLYNOMIALS: In general, degree refers to the highest sum of
exponents of any one term of a polynomial
Example 1: State the degree of each polynomial
a)x3+x2—x+ 1 b)x3÷x2y2+y2÷xy+1 c)m4-m3+m2n3+n2-2
degree: degree: degree:
Example 2: Simplify
a) (3a) (2a) b) (12x) (3X2) (-2x)
1 2x5c) (2m2n3)(np2) d)
3x2
![Page 2: Types of polynomials 3x5y2 I - Home | Sardis Secondary …sss.sd33.bc.ca/sites/default/files/Unit 2 Lessons Master.pdfFMPCIO Unit 2: Polynomials Lesson 1: Multiplying & Dividing Monomials](https://reader031.vdocument.in/reader031/viewer/2022012315/5ac158ed7f8b9a433f8cbd8b/html5/thumbnails/2.jpg)
12m5 28m2n5e)
24m3f)
— 12m2n3
g) (3x2)(2x2)3 I) (—3x2y5)(—4xy3)28x4y4
HW: 2.1 Worksheet Attached
![Page 3: Types of polynomials 3x5y2 I - Home | Sardis Secondary …sss.sd33.bc.ca/sites/default/files/Unit 2 Lessons Master.pdfFMPCIO Unit 2: Polynomials Lesson 1: Multiplying & Dividing Monomials](https://reader031.vdocument.in/reader031/viewer/2022012315/5ac158ed7f8b9a433f8cbd8b/html5/thumbnails/3.jpg)
2.1 Multiplying & Dividing Monomials Worksheet
1! Simplify,.a) (7x2X5x4) N (3aX4a) ic) (—6m3X9m2 ci) (5n2X2n)e) (—8y5)(—7y4) 1) (—7b3X4b) s) — (PX—60) h) (12p5)(—3p3X—’2p)
2! Simplify,a) (6x)(3y) b) (Sp2X4q) c) (—5m3)(—ln) ci) (2cjbX7a)e) (—9rXSrs3) .1) (4c4)(—I 1cr) ) (_2s12X.3st) h) (2b2c3Xbc2)
3+ Simplify.a) (—4abX2b2) b) (6m2n3X—2m3n4) c) (7a2b2X3ab3)ci) (—8p2q5—3pq2) e) (2xy)(3x2y)(4x3y) f) (—3ab)(2ab2Xa2b)
4. Simplify.
a’ i2x b’36,,,6 i
54a8ci’ 521,
‘ 3x2‘ 4rn2
C,—6a2 ‘
e) —24cd3 28in2n5 . —32aNø li’—6c4
A!
-7rn2n3g,
‘ 3p2q2
5. Simplify
a) 36r0s4 b -45x8y 45p9q68r2s2 ‘ 15x4y2 ‘ —14p3q2
ci) (3a4b2X6ab3) e) (4m4n2X6mn9a3b4 —3rn6n6 . (h2y3)(6x3y)
6. 1,) (—3a2bX2a4)2 c) (5y2(S)(334)Z
ci) (_4pq3)(._5p3)2 e) (3m2n3X_21flfl2)3 1) (5x2.v)N3xZ9P
“.
_________
b) c)
ci)j42xy2)! e) o
![Page 4: Types of polynomials 3x5y2 I - Home | Sardis Secondary …sss.sd33.bc.ca/sites/default/files/Unit 2 Lessons Master.pdfFMPCIO Unit 2: Polynomials Lesson 1: Multiplying & Dividing Monomials](https://reader031.vdocument.in/reader031/viewer/2022012315/5ac158ed7f8b9a433f8cbd8b/html5/thumbnails/4.jpg)
FMPCIOUnit 2: Polynomials
Lesson 2: Adding & Subtracting Monomials
In General: When adding and subtracting polynomials you can only add or subtractlike terms. This means that you can only add and subtract terms thathave the same variables raised to the same powers respectively.
Examøle 1: Simplify
a) (2x — 7y) + (8x — 3y) b) (5x + 11) — (2x + 4)
c) (4x2 — 7xy + 3) + (x2 — 5yx + 9) — (x2 + 6xy — 11)
d)Add: 7x2—6x+24x2—3x— 4
Example 2: Simplify and state the degree of the monomial.
a) (4a2 — 3b2) + (2a2 — b2) — (3a2 + 4) =
b) (x2y2—y2) — (4x2y + 3x2y)
—(y2 — 2x2y2 — 2y2x) =
HW: 2.2WorksheetAttached
![Page 5: Types of polynomials 3x5y2 I - Home | Sardis Secondary …sss.sd33.bc.ca/sites/default/files/Unit 2 Lessons Master.pdfFMPCIO Unit 2: Polynomials Lesson 1: Multiplying & Dividing Monomials](https://reader031.vdocument.in/reader031/viewer/2022012315/5ac158ed7f8b9a433f8cbd8b/html5/thumbnails/5.jpg)
2.2 Adding and Subtracting Monomials Worksheet
1. Simplify.a) (6a÷9)÷(4a—5) 1,) (2x—7y)+(Sx—3y)
c) (3m2+4)(7+9m2) d) (+ll)—(2p+4)
e) (17x2—9x)—(6x2—5x) 1) (7k÷31)—(i2k—$1)
2. Simplify.a) (3m2—Sm+9)+(8m2+2m—7)
b) (7a3— 2a2 ÷ Sa) + (—3a3+ 6a2 — 2a)
c)(x2—Sx÷6y)—(4x2+i5x—lly)
d) (512_13t+17)+(9t3_712+31_26)_(l612+51_8)
e) (2÷8a2—a3)+(2a3—3a2—8)—(12 —7a3+5a2)
f) (4x2—lx+3)—(x2—Sx+9)—(8x2+6x—li)
4, Sirnplifi, and state the degree of the polynomiELa) (5x2—3x2y+2y2x—y)—(2xy2—y—5x2+33’X2)
b) (p3q2÷ 7q2p2— 3g,) + (2q — 6p2q2— q2p3)
c) (3rn2—3rn+7)—(2n2--2n+7)
d) (2ab—2ac—2bc)÷(2ca÷2cb—2ba+3)
e) (xy + 3yx + 2x2y — 3xy2)— (2xy ± 2yx2)
5. Mia) 3x2—6x±7 b)7z3—6z2÷z—37x2—2x÷9 2z±4z2_z±4
6. SWtract.a) 5x2y—Jxy+2xy2 1)6rn2n2—4mn÷3rnn3
3x2v ÷ 4xy — 2rn2n2t2rntt — 4mn3
7. Sb plify, and state the degree of the polynomial:,a) (3x2—2y2)÷(y2—2x2)—(4x2÷2)
b)(m2—n2)—(n2—m2)÷(2n2+m2)
c) (4x2y— 2yx) + (3yx2 — 6xy2)— (3x2y2÷ 2y2x2—
ci) (a2b2—b2)— (3b2a+ 2a2b) —(b2— b2a2 — b2a)
![Page 6: Types of polynomials 3x5y2 I - Home | Sardis Secondary …sss.sd33.bc.ca/sites/default/files/Unit 2 Lessons Master.pdfFMPCIO Unit 2: Polynomials Lesson 1: Multiplying & Dividing Monomials](https://reader031.vdocument.in/reader031/viewer/2022012315/5ac158ed7f8b9a433f8cbd8b/html5/thumbnails/6.jpg)
FMPIOUnit 2: Polynomials
Lesson 3: Multiplying Polynomials Part I
Example I: Simplify:
a) 2x(3xy—5)
b) -5x3y(4xy2+ 7x) + llx4y
c) 11(2x+ 3y)—7(3y— llx)
d) 2x(3x2 — 5xy + y2) — 5y2(x—
2y)
HW: 2.3 Worksheet Attached
![Page 7: Types of polynomials 3x5y2 I - Home | Sardis Secondary …sss.sd33.bc.ca/sites/default/files/Unit 2 Lessons Master.pdfFMPCIO Unit 2: Polynomials Lesson 1: Multiplying & Dividing Monomials](https://reader031.vdocument.in/reader031/viewer/2022012315/5ac158ed7f8b9a433f8cbd8b/html5/thumbnails/7.jpg)
2.3 Multiplying A Monomial and a Polynomial Worksheet
1. Smiify.a) 4(5x2 + 10) b) 72a — 5) c) -(3k — 2k)
4) 12(2b2—.3b+9) e) _9(...5ffi2+i?fl_3) 1) 3(8p25p+7)
2. Simplify.a) 3(x+4)+7 b) $(2a—3)÷lJa c) 5(y+2)—7y
d) 4(lm—5)—13 e) —6(3p+2p)÷5p2 f) 7(5x—3y)—$3x
a) 12 5x—4) b) 3a(—7a+2) c) 6p(2p—q)
d) —15n2(6 — 9n) e) 7rn3(3nm +6) f) —8x2(5x ÷ ly)
4. Simplil.a) 3(x +2) + 2(x —6) b) 2(x +9) — 3(x + 7)c) 3(2a÷Wb—2c)—6(a—2b+Sc) d) 3(2m—4n+3)—5(—2rn+5n—I)
5, Simplii’.a) 3x2(x + y) +2x3(3x + 5y) b) 3a3(2a — Sb) — 4a3(2a + 3b
c) 5p2(4p — q) —8p2(2p —7q) 4) 6a3(—3a ÷ 7b —4) — 8a3(2a — 3b +7)6. In a hockey league, each team plays afi other teams 4 iimes. Ifthere are n teams,
wiite a formula for the total number ofgames to be played.
7. Simp1if.a) —2ab2(ab—a2+b) b)3x2y(xy2+xy—y)
c) —Sm2n(3mn÷nm2—n2) 4) 5x(x—y)—231(x+y —1)+y2
e) 2b(b—bc)—2c(b —c)÷(76c—4c2)) 7x(x2—y2)—2xy—2y(x2÷y2)
9. Simplity, and state the degree ofthe polynomiaL
a) 3aTh —?a(a —4)+(5ba2—13a)
I,) 6rn(2mn — n) — 3(m2n — 19mn) + 6n(—Smn — 7m2)
c) 4xy(x + 2y) — $x(2xy — 3y2 — 3y(3x2+ 7xy
4) 5s(3E2—7s+2)+2s(5s2+s—6)+9(s2+6s—4)
e) 4x(5x2
1) Sxy—3y(2x —y)÷7x(Sy —x)+9(x3—2y2)
10. Simpliê,a) (1 la + 3X9a) b) (3x — SX—2x) c) $ 5x(16x + 12)4) (5a2+ 2a — 3X—4a) e) I 2n(3n —7) 1’) 5x(2x2— 6x + 3)
![Page 8: Types of polynomials 3x5y2 I - Home | Sardis Secondary …sss.sd33.bc.ca/sites/default/files/Unit 2 Lessons Master.pdfFMPCIO Unit 2: Polynomials Lesson 1: Multiplying & Dividing Monomials](https://reader031.vdocument.in/reader031/viewer/2022012315/5ac158ed7f8b9a433f8cbd8b/html5/thumbnails/8.jpg)
FMPIO
a) (x+3)(x—2)
b) (2a—4)(a+2)
c) (x+3)2
d) (2x—4)2
Unit 2: PolynomialsLesson 4: Multiplying Polynomials II
Example 1: Simplify:
e) (x—3)(4x2—7x+12)
![Page 9: Types of polynomials 3x5y2 I - Home | Sardis Secondary …sss.sd33.bc.ca/sites/default/files/Unit 2 Lessons Master.pdfFMPCIO Unit 2: Polynomials Lesson 1: Multiplying & Dividing Monomials](https://reader031.vdocument.in/reader031/viewer/2022012315/5ac158ed7f8b9a433f8cbd8b/html5/thumbnails/9.jpg)
f) (x —7) (x + 8) (3x —4)
Example 2: Express the area of the shaded region below as a polynomial.
3x+2y -*E- 2x—y
+y
3x-y
HW: 2.4 Worksheet Attached
![Page 10: Types of polynomials 3x5y2 I - Home | Sardis Secondary …sss.sd33.bc.ca/sites/default/files/Unit 2 Lessons Master.pdfFMPCIO Unit 2: Polynomials Lesson 1: Multiplying & Dividing Monomials](https://reader031.vdocument.in/reader031/viewer/2022012315/5ac158ed7f8b9a433f8cbd8b/html5/thumbnails/10.jpg)
2.4 Multiplying Polynomials Worksheet
1. Find the product.a) (4x÷ lX2x+3) b) (5in—2)6m+ 1) C) (2c—3)4c—5)
d) (3x — 7)(3x + 7) e) 4r + 5X4t — 8) f) 8x — 2X3x 7)
2. Square the binomial.a) (g+h) b)(x+y) c)(i+n) d)(b+c)
e) (p...q) f) (k—I) g) (s•..f) Ii) (u—v)
3. Find the product.a) (3A +y)2 b) (x+5y)2 c) (3a÷2)2 d) (Sx—9)2
e) 4rn—7)2 f) (—4y—1l)2 a) (5t+iO)2 Ii) (_5_6b)Z
4. Find the product.a) (2÷y)(3x+y) b) (3a+bX5a—b) c) (2x—y)(3x+4y)
d) (+3j)(+4i) e) (Sin—2nXlm—n) f) (6x—2yX3x—7y)
5. Find the product.a) (3a + 5b)2 b) (2m — 7n)2 c) (6s — 2i)3 4) (4p — 3q)2
e) (8x—3y)2 f) (—3s—5t)2 g) (—5f÷4g)2 ii) (5y2+7z2)2
6. Find the product.a) (x—y)(x+y) b) (2m÷5n)(2rn—5n) C) (9a—4bX9a+4b)
d) 6x — 2yX6x + 2y e) ç7p + 2q)7p — 2q) fl —12m + 9X—12m —9)
7. Simplify.a) (x_3)x+2)+(2X—5XX I) b) (2x+4(3x—2)+(5X —2X3x—-4)
c) (2m÷3)(3rn÷5)+(rn—7X6m—3)d) (c+2dXc+d)—(C—2d)(C—d)
e) (2a — 5b)(3a + b) — (6a — bX4a + 7b) f) (3x — 2y)(5x —y) — (2x + 5’X3x —
y)
8. Simplify.a) (2x_3)2+(x+2)(3X_S) b) (s—2t)2--(s—31)(4S—S1)
c) (2x — y)(2x + y) — (x —2y)2 d) (7in — 2nX3in + 5n) — (4rn — I in)2
e) (5x —2y)2 — (5x + 2y)2 f) (2x2 + 3Xx2 — 5) — (3x2 ÷ 2)2
9. Find the product.
a) (3x — 1X2x2÷3 ....4) b) (m—.3X4m2—7m+ 12)
c) (2a—5X3a2+8a—9)d)(3p+2)(5p2—6p+2)
10. Find the product.a) (3x+4)(x—5X2X+8) b) (4p—3X2p—7X5P—6)
c) (3x ÷22x— 5)4x —3) d) (2x —5)(3x +4)2
e) 5a — 32t2a — 7) 5m —
![Page 11: Types of polynomials 3x5y2 I - Home | Sardis Secondary …sss.sd33.bc.ca/sites/default/files/Unit 2 Lessons Master.pdfFMPCIO Unit 2: Polynomials Lesson 1: Multiplying & Dividing Monomials](https://reader031.vdocument.in/reader031/viewer/2022012315/5ac158ed7f8b9a433f8cbd8b/html5/thumbnails/11.jpg)
11 * Find the perimeter and area ofeach shaded region.a)
_________
1,)
x-2yr’)1_jS+y
k+y .. H1
12. Simplify,a) 3(m—5)(m+2)c) 5(2p—73p--4)e) 3a(2a — SbX3a + b)
13. Simplify.a) 2(3x+lXx+5)÷4(2x+3XJx+5)b) 5(2m — 4X3m + 2)— 2(4m — lX3m —4)
c) 3(2x + SyX7x — $y) + 5(x ÷ 3y)(2x ÷ 4y)
d) 2(xy— 1)(xy÷ t)—5(xy—2)(xy+ 3)
e) 3(2a — 3bXa + 2b) — 2(3a — 3)2
1) 4(xy—2)2+3(xy+5)2
14. Simplify.a) (2x—$X3x+6)+(3x—2X4x÷9)—(Sx—3)(2x—7)
b) 2(3s÷5)(2s—2)—5(3s2+7s—9)—(s+6)2c) (2x+3X3x2_Sx+4)÷(x_4X2xZ+3x_7)
d) (3m+4Xm—4n—i)—(5m—2)(3m—6n—8)
e) (4y — 5)(3y +2)2—(3y + 2X4y — 5)2
f) 4(3x—2X5x2÷x÷6)—(2x+6X3x—1)2
rxty
Fx,2y
I
F..
I —
c)
Zx
x-y1
r C-’
b) 2(x÷yX3x—5y)ci) 4x(x—ly)(2x—3y)
0 3x(2x +
![Page 12: Types of polynomials 3x5y2 I - Home | Sardis Secondary …sss.sd33.bc.ca/sites/default/files/Unit 2 Lessons Master.pdfFMPCIO Unit 2: Polynomials Lesson 1: Multiplying & Dividing Monomials](https://reader031.vdocument.in/reader031/viewer/2022012315/5ac158ed7f8b9a433f8cbd8b/html5/thumbnails/12.jpg)
FMPCIOUnit 2: Polynomials
Lesson 5: Factoring a GCF
2 (x + y) = this process is called
________________________
2x + = this process is called
______________________
Where the — outside is the
______________
Example 1: Use algebra tiles to factor 2x + 8.
Step I Model the polynomial 2x + 8.
Step 2 Arrange the tiles into a rectangle.The total area of the tiles representsthe product.
Example 2: Use Algebra Tiles to factor the following (sketch a diagram of solution).
a) 3x + 9
b) 4x+1O
c) x2 + 5x
![Page 13: Types of polynomials 3x5y2 I - Home | Sardis Secondary …sss.sd33.bc.ca/sites/default/files/Unit 2 Lessons Master.pdfFMPCIO Unit 2: Polynomials Lesson 1: Multiplying & Dividing Monomials](https://reader031.vdocument.in/reader031/viewer/2022012315/5ac158ed7f8b9a433f8cbd8b/html5/thumbnails/13.jpg)
d) 3x2 + 6x
GCF for a Polynomial
GCF of the coefficients and the lowest power of any variable in every term.
Example 2: Find the GCF of the following:
a) 12, 18 b) 3x2y3,6x3y c) I 5x3, I Ox, 35x
Example 3: Factor
a) 12x+18 +
b) 3x3+5x2—x=
c) 36m4+24m2—60=
d) 5x(a—b)+7(a—b)=
e) 2m(2x+ 1)—5(2x+ 1)=
f) 6a(b—a)+4b(b—a)—7(b—a)=
HW: Pg.155#4,7-12,14,16
![Page 14: Types of polynomials 3x5y2 I - Home | Sardis Secondary …sss.sd33.bc.ca/sites/default/files/Unit 2 Lessons Master.pdfFMPCIO Unit 2: Polynomials Lesson 1: Multiplying & Dividing Monomials](https://reader031.vdocument.in/reader031/viewer/2022012315/5ac158ed7f8b9a433f8cbd8b/html5/thumbnails/14.jpg)
FMPCIOUnit 2: Polynomials
Lesson 6: Factoring Trinomials Part I
Example 1: Factor the following using algebra tiles.
a) x2 + 5x + 6
b) x2 + Sx +4
c) x2 — 5x + 6
d)x2+x—6
e) x2 — 3x — 10
![Page 15: Types of polynomials 3x5y2 I - Home | Sardis Secondary …sss.sd33.bc.ca/sites/default/files/Unit 2 Lessons Master.pdfFMPCIO Unit 2: Polynomials Lesson 1: Multiplying & Dividing Monomials](https://reader031.vdocument.in/reader031/viewer/2022012315/5ac158ed7f8b9a433f8cbd8b/html5/thumbnails/15.jpg)
Example 2: Factor Completely.
a)a2+12a+2O=
b) m2—18m+32=
c)n2+3n—40
d)k2—8y—20
e) 2x2+16x+14
f) 3m3-18m2+27m
g)x2+l3xy+12y2
h) a4-’- 10a2+21
![Page 16: Types of polynomials 3x5y2 I - Home | Sardis Secondary …sss.sd33.bc.ca/sites/default/files/Unit 2 Lessons Master.pdfFMPCIO Unit 2: Polynomials Lesson 1: Multiplying & Dividing Monomials](https://reader031.vdocument.in/reader031/viewer/2022012315/5ac158ed7f8b9a433f8cbd8b/html5/thumbnails/16.jpg)
) (x+y)2+6(x+y)+8
j) (x-i-2y)2—4(x+2y)—12
HW: Pg. 166#4,6,11,14,17,19-21
![Page 17: Types of polynomials 3x5y2 I - Home | Sardis Secondary …sss.sd33.bc.ca/sites/default/files/Unit 2 Lessons Master.pdfFMPCIO Unit 2: Polynomials Lesson 1: Multiplying & Dividing Monomials](https://reader031.vdocument.in/reader031/viewer/2022012315/5ac158ed7f8b9a433f8cbd8b/html5/thumbnails/17.jpg)
FMPIOUnit 2: Polynomials
Lesson 7: Factoring Trinomials Part 2
Example 1: Factor the following.
a) 2x2 + 7x +6 1. Multiply the outside coefficientstogether.
2. Find two numbers that multiply to thisproduct and add to the middlecoefficient.
3. Set up brackets with the firstcoefficient in the front position ofboth sets and the two numbers thatyou found in the last position.
4. Divide any common factors out ofeach set of brackets.
5. Check by expanding
b) 8x2+2x—3
c) 2x2+9x+4
d) 8x2+lOx+3
![Page 18: Types of polynomials 3x5y2 I - Home | Sardis Secondary …sss.sd33.bc.ca/sites/default/files/Unit 2 Lessons Master.pdfFMPCIO Unit 2: Polynomials Lesson 1: Multiplying & Dividing Monomials](https://reader031.vdocument.in/reader031/viewer/2022012315/5ac158ed7f8b9a433f8cbd8b/html5/thumbnails/18.jpg)
e) 3x2—13x—1O
Example 2: Factor Completely.
a) 6a3+26a2—20a
b) 4x2y—l7xy—15y
c) 21x2+25xy—4y2
d) 4x2 — 2lxy — 1 8y2 =
HW: Pg. 177 #12,13, 15, 18,19
![Page 19: Types of polynomials 3x5y2 I - Home | Sardis Secondary …sss.sd33.bc.ca/sites/default/files/Unit 2 Lessons Master.pdfFMPCIO Unit 2: Polynomials Lesson 1: Multiplying & Dividing Monomials](https://reader031.vdocument.in/reader031/viewer/2022012315/5ac158ed7f8b9a433f8cbd8b/html5/thumbnails/19.jpg)
FMPIOUnit 2 Polynomials
Lesson 8: Factoring a Difference of Squares
Expand the following:
(x+ 3)(x—3)
(x + 2) (x —2) =
(3x—5)(3x+ 5)=
What’s the pattern???????????????????????????????????????????
To factor we will use this pattern and work backwards
Example 1: Factor the foNowing
a)x2—9 b)81m2—16
c) 1 6m2 — 1 21n2 d) 6x2 — 150
e) 1 2x3 — 27x f) 63x2y2—
![Page 20: Types of polynomials 3x5y2 I - Home | Sardis Secondary …sss.sd33.bc.ca/sites/default/files/Unit 2 Lessons Master.pdfFMPCIO Unit 2: Polynomials Lesson 1: Multiplying & Dividing Monomials](https://reader031.vdocument.in/reader031/viewer/2022012315/5ac158ed7f8b9a433f8cbd8b/html5/thumbnails/20.jpg)
g) (5m — 2)2 —25
h) x4 — 13x2 + 36
i) Y4 — 5y2 — 36
HW: Pg.194#6, 7, 10-13, 20, 21
![Page 21: Types of polynomials 3x5y2 I - Home | Sardis Secondary …sss.sd33.bc.ca/sites/default/files/Unit 2 Lessons Master.pdfFMPCIO Unit 2: Polynomials Lesson 1: Multiplying & Dividing Monomials](https://reader031.vdocument.in/reader031/viewer/2022012315/5ac158ed7f8b9a433f8cbd8b/html5/thumbnails/21.jpg)
2.1 Multiplying & Dividing Monomials Worksheet Key
_____
La)35x’ b)l2tFc)—54m’ d)10n3 e)56 O—28b4g$t’ h)72p’ 2.a)1$xy b)32pqc)35mn d)14a6e)—45A? fl-44cd 2)63213 bc’ 3s)-Sab’b)-12rn5n7c)2:ia’b d)24jPq e)24x6y’ f)—6a4b44.a)4x’ b)9rn c)—9a’ 4)46 e)4cP f)4n2 g)864b)10p245a)2r432 b)—3x’ c4p’q d)2a’be)—$m’ f)6x5t’ 6.a)54x” b)—12a’°b c$Ss’°s’d)—lOOp’q3e)-24mn’ f)675xyt4 7a)&’y3b)—6? c4a263 d)2x4 e)—16rn’n’ fla’3b”
2.2 Adding and Subtracting Monomials Worksheet Key
K
. tsci tcc.1 ‘Jey. 1.fl÷4bnÜE—1oYO1—o—34rnp÷l— 4x fl—5k + 11, 2.a11n$ — 3m + 2
b)4d+4d+3aC)—3Z3—i+ I7y— 189 — 1St — I e)Sd — 18 0ic2 — Sr ÷ 5
3a)P= 15.Sn — 30 000 1,1547 500; 3125 000; 5280 0001
4,a)1(le — 6x& third b)p’q’ — 3p + Zq; fourth- 3m — 2,9 + 2n;sccond d)3;zero
e)—3xf + 2xy third LaWh’ — Sx ÷ 16b)9z’—2t+1 4s)2fl—7Xy+52Y’b)4mW - 6,wz + 7aut 7.s)-3x - - 2; second
b)3m’; second c)-Sfl + 7zy - - 6xy2;fourth
d)2d9 - 2a’b - 2ab’ - 2b1; fourth 8.Answersmay vary.
2.3 Multiplying A Monomial and a Polynomial Worksheet Key
Eerdses 3-4, page 85i.a)2C1t+40 b)14a—35 c)lók-24k2d)24b2— 36b + 108 e)45m2— 63m +27fl24 — 15p €21 2a)3x + 19 b)24 — 5a eflO — 2y4)28m —33 e)—13 — 12p fl4x — 21y3.a)60x2— 48x b)6a — 2hz2 e)12p1— 6pqd)135n’—90n e)21m4n+42rn3 f)—5’—40x34s)Sx —6 b)-x —3 c)42b — 36c dN6rn — 5Th ÷145.t)9x’ + 13x2yb)—2a4—27a36c)4p3+ Slp’q:d>..34a’ + 66a36— 80a’ 6.2n(n —1)7.sfl2a3b2—
24261_ 2ab3 b)3x’y3+ 3x3y2—
c)Sm2n’— Sm’,? — 15m3n2d$x2— — 7+2ye)2b3-2b2c-29+Shef)7x3-lx/ - fly - Zx’y - 2 8a)66 b)Z’
9s)8a36—72 + iSa; third b)21 mit’ — 33m’n; thir:
c)lxy’- iSx2y; third d)43s’+21s2—38s;thirde)5x3 14x2y— 53vtbirdf)SSxy — 15,2 + 2x’; secondiO.a)99ê + 27a b)1Ox — :6x2 c)40x2+ 30xd)—20a’ — 8a’ + 12a c)3.6n’ — 8AirfllOx’—30x2+15x ils)29p— i8q+29b)—29k—41—75 c)3x’+Sxy—9x—29— i4yd)Sa”- lOOa e)45x’—8x2y—2x’f)30m2n—m’—94mn 12.a)a+5b b)lOa÷4bc)a’÷b’ d)a’—a’b—ah’ —6’ 134 =2icrr÷n)14s)911 cm2 b$& c)8xr2— IGn d)3&+ 14n
![Page 22: Types of polynomials 3x5y2 I - Home | Sardis Secondary …sss.sd33.bc.ca/sites/default/files/Unit 2 Lessons Master.pdfFMPCIO Unit 2: Polynomials Lesson 1: Multiplying & Dividing Monomials](https://reader031.vdocument.in/reader031/viewer/2022012315/5ac158ed7f8b9a433f8cbd8b/html5/thumbnails/22.jpg)
2.4 Multiplying Polynomials Worksheet Key
Key: I.a)8x2+14x+3 b)30m2—7rn —2
c)8c2—22c+ 15 d)9x2—49 e)16t2— 12t—40 4
f)24x2— 62x + 14 2.a)g2 + 2gh + h2 b)x2 ÷ 2xy +
c)m2+2mn÷n2d)b2+2bc÷c2e)p1—2pq+q2f)k2 — 2k! + j2 g)s2 — 2sf + 12 h)u2 — 2uv +
3a)9x2+ 6xy + y2 b)x2 + lOxy + 25y2
c)9a2 + 1 2a + 4 d)25x2 — 90x + 81e)16rn2—56m+49 f)169+88y+ 121
g)25r2 — 1001 + 100 h)25 ÷ 60b + 36b24..a)6x2+Sxy÷y2b)15a2+2ab—b2c)6x2+5xy-4y2d)x2÷7xy+ 12y2e)35m2— I9mn + 2n2 f)18x2 — 48xy + 14y2
5.a)9a2 + 3Oab + 25b2 b)4m2 — 28mn + 49n2
c)36s2 — 24sf + 42 d)16p2— 24pq + 9q2e)64x2— 48xy + 9y2 f)9s2 + 30s1 + 2512
g)25f2—4Ofg + 6g2 h)25y4+ 70y2z1+ 49z2
6.a)x —y b)4m —25n c)81a —16b
d)36x2 — 4y2 e)49p2 — 4q2 f)144m2— 81
7a)3x2 -8x — I b)21x2 — 18x c)12m2— 26m + 36
d)6cd e)—18a2-•5lab+2b2f)9x2—26xy+7y28a)7x2— lix— 1 b)—3s2÷l3st — 1Ir2
c)3x2 + 4xy -- 5y2 d)5m2÷ lllmn — 131,12 e)—4Oxy
f)—7x4 — 1 9x2— 19 9.a )6x4 7x2 — I 5x + 4
b)4m —19m +33m-r36c)6a +a —58a÷45
d)15p3— 8p2—
6p + 4 9)aJEx3+ 2x2 — 128x — 160
b)40p3—218p2÷309p—126 )24x3—62x2--7x÷3O •
d)18x3÷3x2— 88x —80 e)50a3—235a2+ 228a —63
f)125rn3—150m2+60m—8 11a)iOx+2y;
4x2 + 2xy — 4$ b)14x + 6y; lOx2 + l4xy + 2y2
c)16x+ 18;12x2+38x+20 12.,a)3m2—9m—30
b)6x2 — 4xy — 10y2 c)30p2— 145p + 140
d)8x3 — 68x2y+ 84xy2 e)18a3 — 39a2b — 15ab2
f)12x3+ 48x2y+ 48xy213a)30x2+108x+70 b)6rn2—2m--48
c)52x2+ IOlxy — 609 d)—3x2y2— 5xy + 28
e)—12a2÷l5ab—20b2f)7x2y2+l4xy+91
14..a)8x2+ 57x — 69 b}-4s2— 39s — 11
c)8x3 — 6x2 — 26x + 40d)—12m2÷ISmn ÷47m —28n—20e)— 1 2$ + 91 v2 — 39y — 70 f)42x3 — 70x2 + 98x — 54
15a)m2+ tim + 26 b)3m2+ 16m + 28
c)rn3 + 5m2 + 6m — 5 16a)4a2+ 4ab + 4b2b)—5a2+ l2ab — 3b2 c)8a2 ÷ 6ab ÷ 2b2
![Page 23: Types of polynomials 3x5y2 I - Home | Sardis Secondary …sss.sd33.bc.ca/sites/default/files/Unit 2 Lessons Master.pdfFMPCIO Unit 2: Polynomials Lesson 1: Multiplying & Dividing Monomials](https://reader031.vdocument.in/reader031/viewer/2022012315/5ac158ed7f8b9a433f8cbd8b/html5/thumbnails/23.jpg)
ID:A
Polynomials ReviewAnswer Section
MULTIPLE CHOICE SHORT ANSWER
1. B 30. (s—32)(s---l)2. A 31. 7(2z—5)(z—l)3. B 32. 27z3+102z2+6Z+1204. B 33. (7s+8t)(7S—8t)5. A 8(z—5)(z—9)6. C
35. =4(7x—2y)(7x+2Y)7. C
8.A9. D 36. a) The outer rectangle area =(9y)(6y) = 54y2
10. C11.
The inner rectangle has area (5y)(3y) = 15y2
13. B b) The total area of the shaded region is the difference in the areas of the rectangles:14. C 54y2—15y2=39y215.
a)6m2—llm+3 a) 4y2—25 c) 6x2+l3xy+6y2 d) 2a4—a2—10 e) 8x2—16x+4
17 B 37. f) 2p2 —6p+4 g) —22m h) —6m2 —5mn+9m+4n+2n2 i) lOx2 —llx+3 j) 9x2 —4918. A k) 32x2+16x+2 1) 2p2—6p+4 m) 6x+20y
19. D a) (x+4)(x+3) b) (m—5)(m+2) c) (2k÷l)2 d) (2p—3)2 e) (6x—5y2)(6x+5y2)20. B f) (x—2)(x+2)(x2+4) g) 5(2x—3)2 h) (—x—1)(3x+1) i) (m—3n)(3m+4n) j) (x+2)(5x—1)21. B 38. k) (x—S)(x—4) 1) (2x—3)(3x+4) m) (x+3)2 n) (m—9)(m+2) o) (6k+1)222.
p) 2(p2 —6p+8) q) (3x—2y)(3x+2y)(9x2+2y2) r) (x-13)(x+13) s) (x—2)(4x—7) t) —4(y—l)(2y
24. Du) not factorable (prime) v) (x + 3)(x —4— Sy) w) (x
—y — 7)(x
— y + 2)
25.A26. B
27. B
28. B29. B
4
![Page 24: Types of polynomials 3x5y2 I - Home | Sardis Secondary …sss.sd33.bc.ca/sites/default/files/Unit 2 Lessons Master.pdfFMPCIO Unit 2: Polynomials Lesson 1: Multiplying & Dividing Monomials](https://reader031.vdocument.in/reader031/viewer/2022012315/5ac158ed7f8b9a433f8cbd8b/html5/thumbnails/24.jpg)
Name: Class: Date: ID:A
U2Polynomials Review
Multiple ChoiceIdentjfr the choice that best completes the statement or answers the question.
1. Simplify the expression
y2 +8y—6—9y2—24y—26,then factor.
a. —8(y2—2y—4)
b. —8(y2+2y+4)
c. —4(2y2+4y+8)
d. —4(2y2+4y+1)
2. Expand and simplify: (p +3)(p —7)
a. p2—4p—21
b. p2—lOp—21
c. p2+lOp—21
d. p2+4p—21
3. Expand and simplify: (6p + 3)(5p —6)
a. 30p2+21p—18
b. 30p2—21p—18
c. 30p2+51p—18
d. 30p2—51p—18
4. Expand and simplify:(3c + 2)(2c —7) + 3(—2c + 1)(7c —5)
a. —36c2+8c—29
b. —36c2+34c—29
c. —36c2—8c—19
d. —36c2—8c—29
5. Expand and simplify: (2x2 + 5x — 6)(5x2 — 2x + 3)
a. lOx4 +21x3—34x2 +27x—18
b. 10x4+21x3—34x2—3x+18
c. lOx4 +21x3—24x2 +27x+ 18
d. lOx4 —29x3—34x2 +27x— 18
6. Expand and simplify: (8h + 3)(7h2 — 4h + 1)
a. 56h3 —53h2—20h+3
b. 56h3÷11h2—12h+3
c. 56h3—11h2—4h+3
d. 56h3—32h2+8h+3
7. Expand and simplify: (5m — 3n)2
a. 25m2—9n2
b. 25m2—lSmn+9n2
c. 25m2 —3Omn+9n2
d. 25m2+9n2
8. Each shape is a rectangle. Write a polynomial, insimplified form, to represent the area of the shadedregion.
a. 5x2+31x+66
b. 5x2+37x+30
c. 5x2+31x+30
d. 5x2+37x+66
9. Which polynomial, written in simplified form,represents the area of this rectangle?
8x — 4y
a. 8x2—36xy—20y2
b. 8x2+22xy—20y2
c. 16x2+72xy—40y2
d. 8x2+36xy—20y2
x + 5y
1
![Page 25: Types of polynomials 3x5y2 I - Home | Sardis Secondary …sss.sd33.bc.ca/sites/default/files/Unit 2 Lessons Master.pdfFMPCIO Unit 2: Polynomials Lesson 1: Multiplying & Dividing Monomials](https://reader031.vdocument.in/reader031/viewer/2022012315/5ac158ed7f8b9a433f8cbd8b/html5/thumbnails/25.jpg)
Name: ID:A
10. Factor the binomial 44a + 99a2.a. a(44+99a)
b. 11(4a+9a2)c. lla(4+9a)d. 22a(2+9a)
11. Factor the trinomial —33b2 + 99b + 77.
a. —11(3b2—9b+7)
b. —33(b2—3b—7)
c. —11(3b2—9b--7)
d. 33(—b2+27b÷7)
12. Factor the trinomial —24c3d — 40c2d2 — 32cd3.
a. —8cd(3c2— 5cd—4d2)
b. 8cd(3c2+5cd+4d2)
c. 8cd(—3c2+5cd+4d2)
d. —8cd(3c2+5cd+4d2)
13. Identify the greatest common factor of the terms in34 42 23
the trmomial 6s t + 1 2s t — 15s t22a. 6st
b. 3s2t2
c. 3s2t3
d. 3s3t2
14. Factor:t2+9t—36a. (t—2)(t+ 18)b. (t+2)Q—18)c. (t+12)(t—3)d. (t—12)Q÷3)
215. Factor: —84+8z+za. (42+z)(—2+z)b. (—6+z)(14+z)c. (—42+z)(2+z)d. (6+z)(—14+z)
16. Factor: —4d2 — 28d + 240a. —4(d + 3)(d — 20)b. —4(d+5)(d—12)c. —4(d—3)(d+20)d. —4(d—5)(d+12)
17. Complete. (k—D)(k—5)=k2—Dk+135
a. (k—27)(k—22)=k2—5k+135
b. (k—27)(k—5)=k2—32k+135
c. (k—27)(k—32)=k2—5k÷135
d. (k-.27)(k—5)=k2—22k+135
18. Factor: 7n2 — 14n —105a. 7(n+3)(n—5)b. 7(n+15)(n—1)c. 7(n—15)(n+1)d. 7(n—3)(n+5)
19. Which multiplication sentence does this set ofalgebra tiles represent?
_H_____H____
a. (2x—2)(2x+2)
b. (2+2)(2÷2)
c.d. (2x-f-2)(2x+2)
20. Factor: 25x2 ÷ 58x + 16a. (25x+4)(x+4)b. (25x+8)(x+2)c. (5x+4)(5x+4)d. (5x+8)(5x+2)
21. Factor: 48y2—
ll6y+6Oa. (l6y—l2)(3y—5)b. 4(4y—3)(3y—S)c.d. 4(4.y+3)(3y+5)
2
![Page 26: Types of polynomials 3x5y2 I - Home | Sardis Secondary …sss.sd33.bc.ca/sites/default/files/Unit 2 Lessons Master.pdfFMPCIO Unit 2: Polynomials Lesson 1: Multiplying & Dividing Monomials](https://reader031.vdocument.in/reader031/viewer/2022012315/5ac158ed7f8b9a433f8cbd8b/html5/thumbnails/26.jpg)
Name: ID:A
22. Factor: 96w2 + 324w —42a. 6(8w+1)(2w—7)b. 6(8w+7)(2w—1)c. 6(8w—7)(2w+1)d. 6(8w—1)(2w+7)
23. Factor: 121a2+llOa+25a. (lla+5)(lla—5)b. (121a+5)(a+5)
c. (ha—S)2
d. (lla+5)2
24. Factor: 16p2—81q2
a. (4p—9q)2
b. (4p+9q)2c. (16p—9q)(p—9q)
d. (4p+9q)(4p—9q)
25. Factor: 3z4 — 768z2
a. 3z2(z+ 16)(z— 16)
b. 3z2(z+ 16)2
c. z2(z+48)(z—16)
d. 3z2(z—16)2
26. Factor Completely: 162 — 2w4
a. (9—w2)(18—w2)
b. 2(9+w2)(3+w)(3—w)
Written
c. 2(9—w2)2
d. 2(9+w2)2
30. Factor: S2 —33s+32
31. Factor: 14z2—49z+35
32. Expand and simplify: (9z2 — 2z + 10)(3z + 12)
33. Factor: 49s2 — 64t2
27. Determine the area of the shaded region in factoredform.
a. 4(x+12)b. (3x+2)(x+12)c. (3x+12)(x+2)
d. (3x—2)(x—12)
28. For which values of k can 6x2 +k+1 befactored?
a. , 7 only
b. ±5, ±7 only
c. -5, -7 only
d. all integers between -7 and 5, inclusive
29. Which of the following is a factor of the
polynomial 3x2 + 2x —8?
a. 3x+2b. 3x-4c. 3x+4d. x-2
34. Factor. Check by expanding.
8z2 — 112z+ 360
35. Factor.
196x2 — 16y2
3
![Page 27: Types of polynomials 3x5y2 I - Home | Sardis Secondary …sss.sd33.bc.ca/sites/default/files/Unit 2 Lessons Master.pdfFMPCIO Unit 2: Polynomials Lesson 1: Multiplying & Dividing Monomials](https://reader031.vdocument.in/reader031/viewer/2022012315/5ac158ed7f8b9a433f8cbd8b/html5/thumbnails/27.jpg)
Name: ID:A
37. Simplify the following:
(2m—3)(3m—1)
(2y—5)(2y+5)
(2x+3y)(3x+2y)
(a2 +2)(2a2 5)
4(2x—1)2
2(p —1) (p —2)
5(—2m--3n)—3(4m—5n)
—3m (2m + n —3)— 2n (m — n —2)
(5x—3)(2x—1)
(3x+7)(3x—7)
) 2(4x+1)
1) 2(p—1)(p—2)
m) —3(2x—4y)+4(3x+2y)
38. Factor Completely
a) x2+7x+12
6) m2-3m-1O
c) 4k2+4k+1
d) 4p2—12p+9
e) 36x2—25y4
f) x”—16
g) 20x2+60x+45
6) x2_(2x+1)2
9 3m2 —5mn—12n2
j) 5x2+9x—2k) x(x—5)—4(x—5)
6x2—x—12
m) x2+6x+9
n) m2—7x—18
o) 36k2+12k+1
p) 2p2—12p+16
q) 81x4—16y4
r) x2—169
s) 4x2—15x+14
t) y2_(3y_2)2
u) 9m2—l8mn—8n2v) x(x+3)—4(x+3)+5y(x+3)
w) (x—y)2—5(x—y)—14
36. The diagram below shows one rectangle insideanother.
a) Determine the area of each rectangle.b) Determine the area of the shaded region.
a)
6)
c)
e)
I)g)
6)
9
4
![Page 28: Types of polynomials 3x5y2 I - Home | Sardis Secondary …sss.sd33.bc.ca/sites/default/files/Unit 2 Lessons Master.pdfFMPCIO Unit 2: Polynomials Lesson 1: Multiplying & Dividing Monomials](https://reader031.vdocument.in/reader031/viewer/2022012315/5ac158ed7f8b9a433f8cbd8b/html5/thumbnails/28.jpg)
ID:A
Polynomials ReviewAnswer Section
MULTIPLE CHOICE
1. B2.A3. B4. B5.A6. C7. C8.A9.D
10. C11. C12.D13. B14. C15. B16.D17. B18.A19.D20. B21. B22.D23.D24.D25.A26. B27. B28. B29. B
SHORT ANSWER
30. (s—32)(s—1)
31, 7(2z—5)(z—1)
32. 27z3 + 102z2 +6z+ 120
33. (7s+8t)(7s—8t)
34. 8(z—5)(z—9)
35. =4(7x—2y)(7x+2y)
![Page 29: Types of polynomials 3x5y2 I - Home | Sardis Secondary …sss.sd33.bc.ca/sites/default/files/Unit 2 Lessons Master.pdfFMPCIO Unit 2: Polynomials Lesson 1: Multiplying & Dividing Monomials](https://reader031.vdocument.in/reader031/viewer/2022012315/5ac158ed7f8b9a433f8cbd8b/html5/thumbnails/29.jpg)
ID:A
36. a) The outer rectangle area = (9y)(6y) = 54y2
The inner rectangle has area = (5y)(3y) = 15y2
b) The total area of the shaded region is the difference in the areas of the rectangles:
54y2—15y2=39y2
a) 6m2 —llm+3 a) 4y2 —25 c) 6x2 +l3xy+6y2 d) 2a4 —a2 —10 e) 8x2 —16x+4
37. f) 2p2—6p+4 g) —22m h) —6m2—5mn+9m+4n+2n2i) lOx2 —llx+3 j) 9x2—49
k) 32x2+16x+2 1) 2p2—6p+4 m) 6x+20y
a) (x+4)(x+3) b) (m—5)(m+2) c) (2k+l)2 d) (2p—3)2 e) (6x—5y2)(6x+5y2)
f) (x—2)(x+2)(x2+4) g) 5(2x—3)2 h) (—x—1)(3x+l) i) (m—3n)(3m+4n) j) (x+2)(5x—l)
38. k) (x—5)(x—4) 1) (2x—3)(3x+4) m) (x+3)2 n) (m—9)(m+2) o) (6k+l)2
p) 2(p2 —6p+8) q) (3x—2y)(3x+2y)(9x2+2y2) r) (x-13)(x+13) s) (x—2)(4x—7) t) —4(y—l)(2y—l)
u) not factorable (prime) v) (x+3)(x—4—5y) w) (x—y—7)(x--y+2)
2