Algebra IIA Unit III: Polynomials Review
Select the best answer.
1. Which monomial has the highest degree?
A 18a5
B 12a6b
C 9a4b4
D 6a2b2c2
2. Which of the following is a fourth degree trinomial with a leading coefficient of 2?
A x  x2  2x4
B 2x4  8x3  x  2
3. Which of the following is equal to (3x2  4x  3) minus (x2 2x  3)?
A 2x2  2x  6
C 2x2  6x  6
B 2x2  6x
D 4x2  2x
4. Which of the following is equal to (x  3)(2x2  4x  1)?
A 2x3  2x2  11x  3
B 2x3  2x2  13x  3
5. Which of the following is equal to (p  2r)3?
A p3  8r3
C p3  3p2r  3pr2r3
B p3  8pr  8r3
D p3  6p2r  12pr2  8r3
6. Which of the following is equal to (x3  2x2  3x  6) divided by (x 2)?
A x2  3
B x2  x  3
7. Which of the following is NOT a factor of (x3 x2 14x  24)?
A x1
C x3
B x2
D x4
8. Which of the following is the complete factorization of (x4 16)?
A (x2  4)(x2  4)
B (x2  4)(x  2)(x  2)
9. If (2  3) is a root of a polynomial with integer coefficients, which of the following must be another root?
3 2
A 2 3
B
C 2 3
D 3 2
10. Which is a list of all the roots of x3  3x2  28x?
A {7, 0, 4}
B {4, 0, 7}
11. Which is a third degree polynomial with 1 and 1 as its only zeros?
A x3  x2  x  1
C x3  3x2  3x  1
B x3  x2  x  1
D x3  3x2  3x  1
12. Which is a list of all the roots of x3  x2  x  1  0?
A {1, i, i }
B {1, i, i }
13. What is the degree of the simplest polynomial with integer coefficients that has
A 3
B 4
5 and 5i as zeros?
C 5
D 6
14. Given P(x)  4x3  11x2  16x  9, describe the end behavior.
15. Which is a graph of an even function with a positive leading coefficient?
A
B
C
D
16. If f(x)  x2  2x  3, which of the following is equal to g(x)  f(x  1)?
A x2  2
B x2  2x  4
17. Which of the following is a reflection of f(x)  2x3  3x2  4x  5 across the x-axis?
A g(x)  2x3  3x2  4x  5
D k(x)  2x3  3x2  4x  5
B h(x)  2x3  3x2  4x  5
C j(x)  2x3  3x2  4x  5
18. If f(x) is a third degree polynomial function and g(x)  f(2x), which of the following must be
true?
A f(x) and g(x) have the same x-intercepts.
B f(x) and g(x)have the same y-intercept.
19.What is the degree of the polynomial that best fits the data below?
x
1
2
3
4
5
6
y
33
8
1
0
7
32
A 2
C 4
B 3
D 5
20. A quintic polynomial has, at most, how many x-intercepts?
A 3
C 5
B 4
D 6