Polynomial Functions Worksheet With Answer Key Page 3
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17Advanced Algebra Honors
Wkst 6-2: Polynomials and Linear Factors
For each function, determine the zeros. State the multiplicity of any multiple zeros.
3
2
3
1. y = (x − 5)
2.
y = x(x − 8)
3. y = (x − 2)(x + 7)
4
3
2
3
2
4. f(x) = x
− 8x
+ 16x
5.
f(x) = 9x
− 81x
6. y = (2x + 5)(x − 3)
Write each function in standard form.
7. y = (x − 5)(x + 5)(2x − 1)
8. y = (2x + 1)(x − 3)(5 − x)
9. A rectangular box is 24 in. long, 12 in. wide, and 18 in. high. If each dimension is increased
by x in., write a polynomial function in standard form modeling the volume V of the box.
Write a polynomial function in standard form with the given zeros.
10. −1, 3, 4
11. 1, 1, 2
12. −3, 0, 0, 5
13. −2 multiplicity 3
Write each expression as a polynomial in standard form.
2
2
2
14. x(x − 1)
15. (x + 3)
(x + 1)
16. (x + 4)(2x − 5)(x + 5)
Write each function in factored form. Check by multiplication.
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2
4
3
2
3
2
17. y = 2x
+ 10x
+ 12x
18. y = x
− x
− 6x
19. y = −3x
+ 18x
− 27x
Find the zeros of each function. Then graph the function.
20. y = (x + 1)(x − 1)(x − 3)
21. y = (x + 2)(x − 3)
22. y = x(x − 2)(x + 5)
Find the relative maximum, relative minimum, and zeros of each function.
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2
3
2
23. f(x) = x
− 7x
+ 10x
24. f(x) = x
− x
− 9x + 9
Write each polynomial in factored form. Check by multiplication.
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2
3
2
3
2
25. x
− 6x
− 16x
26. x
+ 7x
+ 12x
27. x
− 8x
+ 15x
28. A rectangular box has a square base. The combined length of a side of the square base, and
the height is 20 in. Let x be the length of a side of the base of the box.
a. Write a polynomial function in factored form modeling the volume V of the box.
b. What is the maximum possible volume of the box?
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