Polynomial Functions Worksheet With Answer Key Page 5
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17Advanced Algebra Honors
Wkst 6-3: Dividing Polynomials
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2
Determine whether each binomial is a factor of x
+ 3x
– 10x – 24.
1. x + 4
2.
x − 3
3. x + 6
4.
x + 2
Divide using synthetic division.
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2
3
2
5. (x
− 8x
+ 17x − 10) ÷ (x − 5)
6. (x
+ 5x
− x − 9) ÷ (x + 2)
3
2
3
2
7. (−2x
+ 15x
− 22x − 15) ÷ (x − 3)
8. (x
+ 7x
+ 15x + 9) ÷ (x + 1)
3
2
3
2
9. (x
+ 2x
+ 5x + 12) ÷ (x + 3)
10. (x
− 5x
− 7x + 25) ÷ (x − 5)
5
2
1
4
3
2
4
3
2
11. (x
+ x
− x + 1) ÷ (x − 1)
12.
6
2
− x
x
x
x
x
x
+
−
+
−
÷
−
3
3
3
4
3
2
4
3
2
13. (x
− 5x
+ 5x
+ 7x − 12) ÷ (x − 4)
14. (2x
+ 23x
+ 60x
− 125x − 500) ÷ (x + 4)
Use synthetic division and the Remainder Theorem to find P(a).
3
2
3
2
15. P(x) = 3x
− 4x
− 5x + 1; a = 2
16. P(x) = x
+ 7x
+ 12x − 3; a = −5
3
2
4
3
2
17. P(x) = x
+ 6x
+ 10x + 3; a = −3
18. P(x) = 2x
− 9x
+ 7x
− 5x + 11; a = 4
Divide using long division. Check your answers.
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2
19. (x
− 13x − 48) ÷ (x + 3)
20. (2x
+ x − 7) ÷ (x − 5)
3
2
3
2
21. (x
+ 5x
− 3x − 1) ÷ (x − 1)
22. (3x
− 7x + 6) ÷ (x + 2)
− x
Use synthetic division and the given factor to completely factor each polynomial function.
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2
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2
23. y = x
+ 3x
− 13x − 15; (x + 5)
24. y = x
− 3x
− 10x + 24; (x − 2)
Divide.
3
2
4
3
25. (6x
+ 2x
− 11x + 12) ÷ (3x + 4)
26. (x
+ 2x
+ x − 3) ÷ (x − 1)
4
3
2
5
27. (2x
+ 3x
− 4x
+ x + 1) ÷ (2x − 1)
28. (x
− 1) ÷ (x − 1)
1
4
2
3
2
29. (x
− 3x
− 10) ÷ (x − 2)
30. (3x
− 2x
+ 2x + 1) ÷
x
+
3
31. A box is to be mailed. The volume in cubic inches of the box can be expressed as the
3
2
product of its three dimensions: V(x) = x
− 16x
+ 79x − 120. The length is x − 8. Find
linear expressions for the other dimensions. Assume that the width is greater than the
height.
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