review for algebra test over polynomials… use laws of exponents, distributive property, clt,...
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![Page 1: Review for Algebra Test over Polynomials… Use laws of exponents, Distributive Property, CLT, addition, subtraction, multiplication, and division of polynomials](https://reader035.vdocument.in/reader035/viewer/2022062408/56649eb05503460f94bb6500/html5/thumbnails/1.jpg)
Review for Algebra Test over Polynomials…
Use laws of exponents, Distributive Property, CLT,
addition, subtraction, multiplication, and division of
polynomials. Also, find and use GCF.
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The 2nd power mean…
WRITE THE PARENTHESIS TWICE!
( 3p + 4 ) ( 3p + 4 )
9p2 + 12p + 12p + 16
CLT
+ 24p9p2 + 16
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“subtracted from” means…
(2q + 6 ) goes first!
(2q + 6 ) – ( 7q – 3 )
2q + 6 – 7q + 3Distribute the minus sign.
C.L.T.
– 5q + 9
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To find the degree…
ADD all the powers in the term.
3 + 5 + 1 = 9
Ninth degree
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We are given the perimeter:
12x + 1
To find the missing side, first, look at the x-terms .
4x + 5x + ( ? ) = 12x
3x
Now look at the numbers:
+5 + (– 8) + ( ? ) = 1
positive 4
3x + 4
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Area of a triangle:
2
bhA
3 2(5 ) 4
2
w wA
Do the Power to a Power FIRST!
(multiply the powers…)2 3 25 w 625w
625 4
2
w wA
Multiply & Divide numbers:
25 • 4 ÷ 2 = 50
50w7
When you multiply w6 times w…
add the powers!
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Perimeter means…
ADD ALL SIDES!
Label them.3m + 4
2m – 5
C.L.T.
Add all the m-terms…
2m + 3m + 2m + 3m =
10m
Combine the numbers:
+4 + 4 – 5 – 5 = – 2
– 2
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Binomial (2 terms) times a Trinomial (3 terms) means…
6 multiplications
b • b2 = b3
b • 2b = 2b2
b • (–5) = –5b
b3 + 2b2 – 5b
3 • b2 = 3b2
3 • 2b = 6b
3 • (–5) = –15
+ 3b2 + 6b – 15 CLTHighest power first!
b3 + 5b2 + 1b – 15
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Add the powers!Add the powers!
= x12
Multiply the powers!Multiply the powers!
= x12
Subtract the powers!Subtract the powers!
= x12
The zero power means…The zero power means…11
The negative power means…The negative power means…the reciprocal.the reciprocal.
(the x(the x1212 moves to the moves to the numerator)numerator)
= x12
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Area of square:
A = length • widthc + 6
( c + 6 ) ( c + 6 )
c2 + 6c + 6c + 36CLT
+ 12cc2 + 36
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2x2 – 2xy + 3xy – 3y2
CLT+ xy2x2 – 3y2
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4n2 – 6n + 6n – 9CLT
4n2 – 9
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Volume of a rectangular prism:
V = Bh (B is the area of the base)The “base” is a rectangle… length • width
V = l•w•h(2xy4)(3x2y)( x + y )Multiply the first
2 monomials…
Multiply #’s and ADD the Powers!
6x3y5 ( x + y )Distributive
Property
6x4y5 + 6x3y6
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Sum means ADD.
CLT1y2 + 1y2
2y2
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Product means MULTIPLY!
n2 + 5n + 4n + 20CLT
+ 9nn2 + 20
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Perimeter means ADD ALL
SIDES!
Label them.
p2 – 2p + 3
6p + 1
Do not use the 5p. Do not use the 5p. That’s the height.That’s the height.
CLTStart with the highest power.
p2 + p2
2p2
(-2p) + (-2p) + 6p + 6p
+ 8p
+3 + 3 + 1 + 1
+ 8
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The GCF consists of:
The biggest number that will divide into 8 and 12…
4
and the common/shared variables… c and d
Take the lowest power.
c2 and
c d2 3
d3
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a. NOT Like Terms… Cannot be simplified!
b. Multiply #’s and… Add the powers.
= 24x7
c. Power to a power… Multiply the powers.
(x0)7 = x0
Anything to the 0 power equals 1.24 • 1 =
= 24d. NOT Like Terms… Cannot be simplified!
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GCF consists of:
The biggest number that will go into 20 and 30…
10
AND, the common variable(s) with the LOWEST POWER…
y6
10y6 ( )
Divide both terms by 10y6 and put the results
in the parentheses.
10y6 10y6
2 + 3
y (8 – 6)
y2
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Quadratic 2nd power Trinomial 3 terms
TRUE
Cubic 3rd power Binomial 2 terms
FALSE
5th degree 5th power Monomial 1 term
TRUE
linear 1st power Binomial 2 terms
TRUE
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Distributive Property
Multiply the #’s and add the powers!
15x4 + 6x2
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Multiply #’s and Add the powers: 6m –
2
n0 equals 1…GOES AWAY!
m–2 means…the reciprocal.
(It goes in the bottom)
26m
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Distributive Property
Distribute the minus sign.
– 7d2 – d + 5d2 – 4d + 3 CLTCLT
– 6d2 – 5d + 8
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a2 – 5a + 5a – 25 TRUE
ADD…CLT a + a + 5
2a + 5
FALSE
( a + 5 ) ( a + 5 )a2 + 5a + 5a + 25
a2 + 10a + 25
FALSE
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12x2 + 18x – 10x – 15 CLT + 8x12x2 – 15
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Area of a rectangle:
A = bh
We know A and b.
To solve for h…
divide!3 236 12
12
x x
x
3x2 + x
36 ÷ 12
x(3 – 1)
12 ÷ 12
x(2 – 1)
A
b
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20 ÷ 4
g(10 – 3)
5g7
– 4 ÷ 4
g(7 – 3)
– 1g4
28 ÷ 4
g(3– 3) = g0 = 1
+ 75g7 – g4 + 7
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The power outside the
parentheses applies to
everything in parentheses.
43 = ?
64
Power-to-a-Power:Multiply powers!
a6•3 = ?
a18
b5•3 = ?
b15
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6k3 + 4k – 10 – 5k2 – 6k + 9CLT
6k3 – 5k2 – 2k – 1
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STUDY!STUDY!