### About Finding the Zeros of a Polynomial Function:

When we are asked to find the zeros of a polynomial function, we are trying to find the x-value or x-values for which the function is equal to zero.

Test Objectives
• Demonstrate the ability to find the zeros for a polynomial function
Zeros of a Polynomial Function Practice Test:

#1:

Instructions: Find all zeros.

a) f(x) = x3 + 5x2 + 8x - 96

b) f(x) = x3 - x2 - 53x + 165

#2:

Instructions: Find all zeros.

a) f(x) = x3 - 2x2 - 16x + 32

b) f(x) = x4 - 5x3 + 11x2 - 15x

#3:

Instructions: Find all zeros.

a) f(x) = x5 + 2x4 - 18x3 - 36x2 + 81x + 162

b) f(x) = x4 + 16x3 + 54x2 - 16x - 55

#4:

Instructions: Find all zeros.

a) f(x) = x4 + 5x3 - 8x - 40

b) f(x) = x4 + 6x3 + 6x2 - 12x - 16

#5:

Instructions: Find all zeros.

a) f(x) = x4 + 8x3 + 11x2 - 32x - 60

b) f(x) = x5 + x4 - 5x3 + 5x2 + 4x - 6

Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}-4 \pm 4i, 3$$

$$b)\hspace{.2em}-2 \pm \sqrt{37}, 5$$

#2:

Solutions:

$$a)\hspace{.2em}\pm 4, 2$$

$$b)\hspace{.2em}0, 3, 1 \pm 2i$$

#3:

Solutions:

$$a)\hspace{.2em}-2, 3 \hspace{.1em}\text{mult.}\hspace{.1em}2, -3 \hspace{.1em}\text{mult.}\hspace{.1em}2$$

$$b)\hspace{.2em}\pm 1, -11, -5$$

#4:

Solutions:

$$a)\hspace{.2em}-5, 2, -1 \pm i \sqrt{3}$$

$$b)\hspace{.2em}-4, -2, \pm \sqrt{2}$$

#5:

Solutions:

$$a)\hspace{.2em}-5, -3, \pm 2$$

$$b)\hspace{.2em}\pm 1, -3, 1 \pm i$$