COURSE 3 LESSON 12-9
Adding and Subtracting Polynomials
Name the coefficients in each polynomial.
a.
b.
7 is a constant
–5
–1
4
6 –1
–x = –1 • x
The coefficients are
–5 and –1.
The coefficients are
4, 6, and –1.
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COURSE 3 LESSON 12-9
Adding and Subtracting Polynomials
Add: (5p2 + 2p + 7) + (2p2 – p – 5).
Method 1 Add using tiles.
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COURSE 3 LESSON 12-9
Adding and Subtracting Polynomials
(continued)
Method 2 Add using properties.
(5p2 + 2p + 7) + (2p2 – p – 5)
= (5p2 + 2p2) + (2p – p) + (7 – 5)
Group like terms.
= (5 + 2)p2 + (2 – 1)p + (7 – 5)
Use the Distributive Property.
= 7p2 + p + 2
Simplify.
Check Check the solution in Example 2 by substituting 1 for p.
(5p2 + 2p + 7) + (2p2 – p – 5)
(5 • 12 + 2 • 1 + 7) + (2 • 12 – 1 – 5)
(5 + 2 + 7) + (2 – 1 – 5)
7p2 + p + 2
(7 • 12 + 1 + 2)
Substitute 1 for p.
(7 + 1 + 2)
Multiply.
10 = 10
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Add.
COURSE 3 LESSON 12-9
Adding and Subtracting Polynomials
A garden has sides of 3x + 5, 4x – 2, 5x + 2, and 7x – 6. Write
a polynomial to express the length of edging that is needed to go
around the garden.
To find the perimeter of the garden, find the sum of the four sides.
perimeter = (3x + 5) + (4x – 2) + (5x + 2) + (7x – 6)
= (3x + 4x + 5x + 7x) + (5 – 2 + 2 – 6)
Group like terms.
= 19x – 1
Add the
coefficients.
The perimeter of the garden is (19x – 1). The edging must be (19x – 1)
units long to go around the garden.
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