TEST 5 REVIEW: Polynomials 5.1 – 5.4
Name __________________________
1) Find the sum of (5x5 + 2x4 – 4x + 7) and (3x5 – 7x4 + x3 + 9).
2) Subtract (2x2 – 5x –1) from (8x2 – 3).
3) Subtract (–x3 + 2x + 4) from (x3 – 3x2 + 1)
4) –4x4(3x2 – 6x + 5) =
5) (4x – 3)2 =
6) (x + 2)(x – 1)(x – 3) =
7) (x – 4)(x + 3)(x – 2) =
8) Divide: (x3 + 7x2+ 8x – 6) ÷ (x2 + 3x – 1) =
9) Divide: (2x3 – 5x2+ 3) ÷ (x2 – 2x + 5) =
10) Divide (3x2 – 5x + 7) ÷ (x – 5) =
11) Divide: (x2 + 10) ÷ (x + 5) =
Let f(x) = 3x2 – 5x + 7. f(5) = ________
Let f(x) = x2 + 10. f(-5) = _________
12) Describe the end behavior of the graph of the function f(x) = –3x4 – 1x3 + 7x2 + 2x + 4
f(x) approaches __________ as x approaches +∞, and f(x) approaches ________ as x approaches –∞.
13) Describe the end behavior of the graph of the function f(x) = 4x5 – x3 + 8x2 – 4x.
f(x) approaches __________ as x approaches +∞, and f(x) approaches ________ as x approaches –∞.
14) For f(x) = 4x3 – 3x – 2x4 + 2, write it in standard form and describe the degree, type and leading coefficient of the
function.
Standard Form: ___________________________________ Leading coefficient: _________
Degree: _________ Type : ____________________
Review vocabulary:
Degree 1  type =
degree 2  type =
Degree 3  type =
degree 4  type =
15) Factor Completely.
x4 – 7x2 + 10 =
8x3 + 27 =
x3 – 125 =
3x3 + 15x2 – 4x – 20 =
27x3 – 125 =
x3 – 9x2 – 10x =
x3 + 216 =
2x3 + 9x2 – 5x =
16) Is (x + 2) a factor of f(x) = –2x3 + 8x2 – 10x + 20? How do you know? Explain.
17) Determine the value of k for the equation below so that the given x-value is a solution.
a. x3 + 5x2 – 8x – 2k = 0; x = 2
b. 3x3 – 11x2 – kx + 8 = 0; x = 4
18) The volume V (in cubic feet) of an aquarium is modeled by the polynomial function V(x) = x3 + 2x2 – 13x + 10, where x
is the length of the tank.
a. Show that x – 1 is a factor of V(x) using synthetic division.
b. Factor V(x) completely.