SMIII Chapter 6 Review
Name: ____________________________________
Pd: _________
Definitions: Choose the best definition for each term.
𝑝
1. Average rate of change
a. A root of a polynomial must be of the form 𝑞 , where p is a factor of
2. Remainder Theorem
3. Factor Theorem
4. Rational Root Theorem
the constant term and q is a factor of the leading coefficient.
b. Every polynomial equation of degree n must have n roots.
c. The ratio of the independent variable to the dependent variable
over a specific interval (a, b).
d. A polynomial has a linear polynomial as a factor if and only if the
remainder is 0, therefore f(r) = 0 if (x-r) is a factor.
e. None of these
Determine the average rate of change for the given interval for each polynomial function.
5. (1, 2)
6. (-2, 0)
Give the factor that corresponds to the zero.
7. -12
8. 6
Give the zero that corresponds to the factor
10. x + 10
11. x - 5
The graph models the number of gallons of water that are
filtered at a filtration plant hourly.
13. How many gallons of water has the plant filtered
after running for about 10 hours?
14. Where is this information from question #13 located
on the graph?
15. The plant filtered 450 gallons of water at which
hours?
16. What is the greatest number of gallons of water that
was filtered within the interval (0, 28)?
17. Where is the information from question #16 located
on the graph?
9. 0
12. x2
Determine if the given factor is a factor of each polynomial using Long Division, or Synthetic Division if possible.
18. Is x + 2 a factor of 2x3 + x – 6
7
19. True (A) False (B) (𝑥 2 − 2𝑥 + 4) ÷ (𝑥 + 1) = 𝑥 − 3 + 𝑥+1
Determine each function value using the Remainder Theorem.
20.
21. Use the Factor Theorem to determine whether the given expression is a factor of each polynomial.
22. What is the greatest common factor?
Factor completely.
23. x2 + 4x - 12
26. - x2 - 7x + 30
24. x2 - 16x - 36
25. 4x2 + 7x + 3
27. x3 - 12x2 - 28x
28. x3 - 3x2 - 4x + 12
Given f(x) = x3 – 3x2 – 13x + 15, answer these questions.
29. What is a ‘p’ value of f(x)?
30. What is a ‘q’ value of f(x)?
31. What is a possible root of f(x) according to the Rational Root Theorem?