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Chapter 4.1- 4.2 Review Worksheet
1. Divide 8x2 – 2x + 4 by 4x – 3 using long division
2. Use synthetic division to divide 2x4 – 7x3 – 2x2 + 1 by x – 3
3. If P(x) = 4x3 – 8x2 + 3x + 1, Find P(–1) using synthetic division
4. If P(x) = 9x4 – 16ix3 + x + (7 – i) find P(i)
5. Graph F(x) = – x3 – 2x2 + 2x + 1 using
synthetic division between – 3 ≤ x ≤ 2 and find:
lim 𝐹(𝑥) =
𝑥 → −∞
lim 𝐹(𝑥) =
𝑥→∞
6. Find all zeros of f(x) = x3 + 7x2 + 11x + 2
7. Write the zeros of each polynomial. Indicate the multiplicity of each if over one. What is the
degree of each polynomial?
a) P(x) = (x – 7)2 (x + 1)4
Zeros:
Degree ____
b) P(x) = 4(x – 1) (x – 2)2
Zeros:
Degree ____
c) P(x) = x(x – 3)3 (x + 4)7 (x – 7)2 (x – 2)
Zeros:
Degree ____
8. Find a polynomial of lowest degree, with leading coefficient 1 that has the indicated graph.
Assume all zeros are integers. Leave in factored form. Indicate the degree of each polynomial.
2
4
6
8
9. Divide 10x4 – 7x3 + 6x2 + 3x – 7 by 5x2 – x – 2
10. Graph P(x)= x3 - 2x2 - 3x + 6; −2 ≤ 𝑥 ≤ 3
Number of intercepts? _________
Number of turning points?_________
11. Using long division, divide 3x3 – 8x2 + 15 by 3x – 5
12. Given Q(x) = 6x3– 4x2 + 2x – 8. Using synthetic division divide Q(x) by x + 2.
13. Use the graph to guess possible linear factors of H(x). Then completely factor H(x) with
the aid of synthetic division. H(x)= 3x3 – 5x2 – 24x - 16
14. (a) Describe the end behavior of Z(x) = 4x4 + 2x3 – x5 – 5x + 16
lim 𝑍(𝑥) =
lim 𝑍(𝑥) =
𝑥→∞
𝑥 → −∞
(b) Describe the end behavior of S(x)= x4 + 9x3 – 14x – 10
lim 𝑆(𝑥) =
𝑥→∞
lim 𝑆(𝑥) =
𝑥 → −∞
15. If P(x) = 2x3 – 5x + 10, find P(-2) using synthetic division and the remainder theorem.
16. Given the polynomial P(x) = x3(x – 5)5(x + 3)2(x – 17), find all zeros
17. Use the Rational Zeros Theorem to write a list of all potential rational zeros.
F(x) = 4x3 – 3x2 + 8x – 6
18. Find all rational zeros. M(x)= 4x3 – 11x2 – 54x + 45
19. Write a polynomial function in factored form of minimum degree with real coefficients
whose zeros include those listed. Leave answers in factored form.
a. 4 (mult 3), 0, and 9 – 2i
4
b. (mult 2), -3, 0(mult 4), 2, and -1(mult 3).
5