Download Chapter 5 Review

Name
Class
Ch 5
Date
Review
Carpenter
Polynomial Functions
Write each polynomial in standard form. Then classify it by degree and by number of terms.
1.
3.
3 + 3x  3x
6  2x3  4 + x3
2.
1  2s + 5s4
4.
a3(a2 + a + 1)
Determine the end behavior of the graph of each polynomial function.
5.
y = 3x4 + 6x3  x2 + 12
6.
y = 50  3x3 + 5x2
7.
y = 12x4  x + 3x7  1
y = 20  5x6 + 3x  11x3
8.
Describe the shape of the graph of each cubic function by determining the end
behavior, zeros, and turning points. Use these to sketch the graph.
10. y = 2x3 + 3x  1
9. y = x3 + 4x
Determine the sign of the leading coefficient and the degree of the polynomial
function for each graph.
12.
11.
Write each polynomial in factored form. Check by multiplication.
13.
2x3 + 10x2 + 12x
14.
x4  81
15.
3x3 + 18x2  27x
16.
8x3  27
17.
x3 + 7x2 - 9x - 63
18.
x2  4 x  4  y 2
Write a polynomial function in standard form with the given zeros.
19.
x = 3, 0, 0, 5
Find the zeros of each function. State the multiplicity of multiple zeros.
20.
y = (5x  2)(2x + 7)3
21.
y = x4  8x3 + 16x2
Find the real or imaginary solutions of each equation by factoring.
22.
2x3 + 54 = 0
23.
4x3  32 = 0
24.
x4  10x2 + 16 = 0
25.
x4 + 13x2 + 36 = 0
Find the real solutions of each equation by graphing.
26.
2x4 = 9x2  4
Divide using synthetic division.
27.
(2x4 + 23x3 + 60x2  125x  500) ÷ (x + 4)
Use synthetic division and the given factor to completely factor each polynomial function.
28.
y = x3 + 4x2  9x  36; (x + 3)
29. The expression V(x) = x3  13x + 12 represents the volume of a rectangular safe in
cubic feet. The length of the safe is x + 4. What linear expressions with integer
coefficients could represent the other dimensions of the safe? Assume that the height
is greater than the width.
Use synthetic division and the Remainder Theorem to find P(a).
30.
P(x) = 2x4  9x3 + 7x2  5x + 11; a = 4
Write a polynomial function with rational coefficients so that P(x) = 0 has the
given roots.
31.
3i and
6
What does Descartes’ Rule of Signs say about the number of positive real roots
and negative real roots for each polynomial function?
32. P(x) = 2x4  x3  3x + 7
Use the rational root theorem to find all roots for P(x) = 0.
33.
P(x) = 2x3 + 13x2 + 17x  12
Expand each binomial.
35.
(n  6)5
36.
(2b + c)4
34.
P(x) = x4  2x3  x2  4x  6
Find the specified term of each binomial expansion.
seventh term of (x  2y)6
37.
Find a polynomial function whose graph passes through each set of points.
38.
(4, 1) and (3, 13)
40.
(0, 9), (2, 21) (1, 0), and (3, 36)
39.
(2, 12), (1, 6), and (2, 24)
Determine the cubic function that is obtained from the parent function y = x3 after
each sequence of transformations.
41. a reflection in the x-axis;
a vertical translation 3 units down;
and a horizontal translation 2 units right
42. a vertical stretch by a factor of 3;
a reflection in the x-axis;
a vertical translation 2 units up;
and a horizontal translation 2 units left
Find all the real zeros of each function.
43.
y = 3(x  2)3 + 24
44. y  
1
( x  4)3  1
2
Find a quartic function with the given x-values as its only real zeros.
45.
x = 2 and x = 8