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Chapter 5 Study Guide
Write each polynomial function in standard form. Then classify it by
degree and by number of terms.
1. 6x5 − 2x2 + 1 − 2x5
2. x2 − 3x + 6x3 − 5x + 1
Determine the end behavior and y-intercept of the graph of each
polynomial function.
3. y = 3x + 2x2 − 4
4. y = 4x3 − 7x + 2
Find the zeros of each function. State the multiplicity of multiple zeros.
5. y = (x + 2)(x − 3)2
6. y = x3 + 4x2
Find the real solutions of each equation using a graphing calculator.
Where necessary, round to the nearest hundredth.
7. 5x3 – 2x2 – 1 = 0
8. 2x4 + 4x2 = 4
Divide using synthetic division.
9. (x2 + 6x + 24) ÷ (x + 4)
10. (x3 + 2x2 + 4x + 10) ÷ (x + 1)
Write a polynomial function with rational coefficients with the given
roots.
11. –1, 2, 6
12. –i,
2
(remember, roots and imaginary #’s come in pairs)
Find all the zeros of each function by factoring.
13. y = x3 + 2x2 + 4x + 8
14. y = x4 – 14x2 + 45
Expand each binomial.
15. (x + 2)6
16. (2x + 3)5
17. On graph paper, sketch the graph of the polynomial.
Be sure to carefully graph the zeros, y-intercept, and use
your calculator to determine the relative minimum and
maximum to the nearest tenth. Be sure to list as an
ordered pair. f(x) = -x³ + x² +3x - 2
20. The product of three integers is 56. The second number is
twice the first number. The third number is five more than the
first number. What are the three numbers?
21. What is P(2) given that P(x) = 3x4 – x3 + 2x2 – 10?
Use synthetic division.