holt algebra 1 7-6 adding and subtracting polynomials warm up simplify each expression by combining...
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Holt Algebra 1
7-6 Adding and Subtracting Polynomials
Warm UpSimplify each expression by combining like terms.
1. 4x + 2x
2. 3y + 7y
3. 8p – 5p
4. 5n + 6n2
Simplify each expression.
5. 3(x + 4)
6. –2(t + 3)
7. –1(x2 – 4x – 6)
6x
10y
3p
not like terms
3x + 12
–2t – 6
–x2 + 4x + 6
Holt Algebra 1
7-6 Adding and Subtracting Polynomials
Graph the line given the slope and y-intercept.
x
yslope = 4; y-intercept =
4
1
RISE
RUN
4
1
Holt Algebra 1
7-6 Adding and Subtracting Polynomials
Students will be able to: Add and subtract polynomials.
Learning Target
Holt Algebra 1
7-6 Adding and Subtracting Polynomials
Just as you can perform operations on numbers, you can perform operations on polynomials. To add or subtract polynomials, combine like terms.
Holt Algebra 1
7-6 Adding and Subtracting Polynomials
Add or Subtract..
A. 12p3 + 11p2 + 8p3
12p3 + 11p2 + 8p3
20p3 + 11p2
B. 5x2 – 6 – 3x + 8
5x2 – 6 – 3x + 8
5x2 – 3x + 2
C. t2 + 2s2 – 4t2 – s2
t2 + 2s2 – 4t2 – s2
–3t2 + s2
D. 10m2n + 4m2n – 8m2n
10m2n + 4m2n – 8m2n
6m2n
E. 2s2 + 3s2 + s
2s2 + 3s2 + s
5s2 + s
F. 4z4 – 8 + 16z4 + 2
4z4 – 8 + 16z4 + 2
20z4 – 6
Holt Algebra 1
7-6 Adding and Subtracting Polynomials
G. 2x8 + 7y8 – x8 – y8
Add or subtract.
2x8 + 7y8 – x8 – y8
x8 + 6y8
H. 9b3c2 + 5b3c2 – 13b3c2
9b3c2 + 5b3c2 – 13b3c2
b3c2
Holt Algebra 1
7-6 Adding and Subtracting Polynomials
Polynomials can be added in either vertical or horizontal form.
In vertical form, align the like terms and add:
(5x2 + 4x + 1) + (2x2 + 5x + 2)
= 7x2 + 9x + 3
5x2 + 4x + 1+ 2x2 + 5x + 2
7x2 + 9x + 3
Holt Algebra 1
7-6 Adding and Subtracting Polynomials
Add.
A. (4m2 + 5) + (m2 – m + 6)
5m2 – m + 11
B. (10xy + x) + (–3xy + y)
7xy + x + y
C. (6x2 – 4y) + (3x2 + 3y – 8x2 – 2y)
x2 – 3y
D.
Holt Algebra 1
7-6 Adding and Subtracting Polynomials
Add (5a3 + 3a2 – 6a + 12a2) + (7a3 – 10a).
12a3 + 15a2 – 16a
–(2x3 – 3x + 7)= –2x3 + 3x – 7
Distribute.
Subtract.
(x3 + 4y) – (2x3)
–x3 + 4y
Holt Algebra 1
7-6 Adding and Subtracting Polynomials
Subtract.
(7m4 – 2m2) –(5m4 – 5m2 + 8)
2m4 + 3m2 – 8
4 2 4 27 2 5 5 8m m m m
Holt Algebra 1
7-6 Adding and Subtracting Polynomials
Subtract.
(–10x2 – 3x + 7) – (x2 – 9)
–11x2 – 3x + 16
2 210 3 7 9x x x
Holt Algebra 1
7-6 Adding and Subtracting Polynomials
Subtract.
(9q2 – 3q) – (q2 – 5)
2 2
2
9 3 5
8 3 5q
q q q
q
Holt Algebra 1
7-6 Adding and Subtracting Polynomials
Subtract.
(2x2 – 3x2 + 1) – (x2 + x + 1)
2 2 2
2
2 3 1
2
1x x x
x
x
x
Holt Algebra 1
7-6 Adding and Subtracting Polynomials
The profits of two different manufacturing plants can be modeled as shown, where x is the number of units produced at each plant.
Use the information above to write a polynomial that represents the total profits from both plants.
–0.03x2 + 25x – 1500
–0.02x2 + 21x – 1700+
–0.05x2 + 46x – 3200
HW pp. 487-489/17-53 Odd,54-56,63-72