NAME
DATE
8-1
PERIOD
Practice
Adding and Subtracting Polynomials
Find each sum or difference.
1. (4y + 5) + (-7y - 1)
2. (-x2 + 3x) - (5x + 2x2)
-3x2 - 2x
-3y + 4
3. (4k2 + 8k + 2) - (2k + 3)
4. (2m2 + 6m) + (m2 - 5m + 7)
4k2 + 6k - 1
5. (5a2 + 6a + 2) - (7a2 - 7a + 5)
3m2 + m + 7
6. (-4p2 - p + 9) + ( p2 + 3p - 1)
-2a2 + 13a - 3
7. (x3 - 3x + 1) - (x3 + 7 - 12x)
-3p2 + 2p + 8
8. (6x2 - x + 1) - (-4 + 2x2 + 8x)
4x2 - 9x + 5
9x - 6
9. (4y2 + 2y - 8) - (7y2 + 4 - y)
10. (w2 - 4w - 1) + (-5 + 5w2 - 3w)
-3y2 + 3y - 12
6w2 - 7w - 6
Determine whether each expression is a polynomial. If it is a polynomial, find the
degree and determine whether it is a monomial, binomial, or trinomial.
11. 7a2b + 3b2 - a2b
1 3
12. −
y + y2 - 9
5
yes; 3; binomial
x + 3x4 - 21x2
x
14. −
3
yes; 6; monomial
not a polynomial
Write each polynomial in standard form. Identify the leading coefficient.
15. 8x2 - 15 + 5x5
5
16. 10x - 7 + x4 + 4x3
2
x4 + 4x3 + 10x -7; 1
5x + 8x -15; 5
17. 13x2 - 5 + 6x3 - x
18. 4x + 2x5 - 6x3 + 2
6x3 + 13x2 - x - 5; 6
2x5 - 6x3 + 4x + 2; 2
19. BUSINESS The polynomial s3 - 70s2 + 1500s - 10,800 models the profit a company
makes on selling an item at a price s. A second item sold at the same price brings in a
profit of s3 - 30s2 + 450s - 5000. Write a polynomial that expresses the total profit from
the sale of both items. 2s3 - 100s2 + 1950s - 15,800
20. GEOMETRY The measures of two sides of a triangle are given.
If P is the perimeter, and P = 10x + 5y, find the measure of
the third side. 2x + 2y
Chapter 8
8
3x + 4y
5x - y
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
13. 6g2h3k
yes; 3; trinomial