GSE Algebra II – Unit 3A Polynomial Functions Analysis
Name: ________________________
Remedial Practice
1) [MGSE9-12.N.CN.9] Using the Rational Root Theorem, list all possible rational roots for the function f(x)= 5x3 + 4x + 14
2) [MGSE9-12.N.CN.9] According to the Fundamental Theorem of Algebra, how many roots does the polynomial
3x 4  7 x 3  24 x  15 have?
3) [MGSE9-12.A.APR.2] Is -2 a root of p( x)  x 3  5x 2  10 x  30 ?
4) [MGSE9-12.A.APR.2] Arnold is attempting to find factors of the polynomial f ( x)  x 3  5x 2  x  5 by applying the
Remainder Theorem. He used synthetic division and the results are shown below. Based on the results of the synthetic
division, what can Arnold conclude?
5 1  5 1 5
5
0 5
1 0 1 0
(A) ( x  5) is a factor because the remainder is zero.
(B) ( x  5) is a factor because the remainder is not zero.
(C) ( x  5) is not a factor because the remainder is not zero.
(D) ( x  5) is a factor because the remainder is zero.
---------------------------------------------------------------------------------------------------------------------------------------------------------------5) [MGSE9-12.N.CN.8] If -6 - 8i is a root of a function what other complex number must also be a root of the function?
6) [MGSE9-12.A.SSE.2] What is the Greatest Common Factor of the terms of this polynomial?
18x 5  6 x 4  30 x 3
7) [MGSE9-12.A.SSE.2] Factor
x 2  2 x  35 ?
8) [MGSE9-12.A.SSE.2] Factor
36 x 2 121 
9) [MGSE9-12.A.SSE.2] Factor 2 x  9 x  35 ?
2
10) [MGSE9-12.A.APR.2] If -8 is a root of the polynomial p(x) , then what must be a factor of p(x) ?
11) [MGSE9-12.A.APR.2] Archer has determined that f (7)  0 , where f is a polynomial function. What theorem
tells Archer that x  7 is a factor of f ?
12) [MGSE9-12.A.SSE.1] What is the name of a 3rd degree polynomial?
What is the name of a 2rd degree polynomial?
What is the name of a 4th degree polynomial?
What is the name of a polynomial with 3 terms?
What is the name of a polynomial with 2 terms?
14) [MGSE9-12.N.CN.8] Create a polynomial that has the factor x  4  2i ?