Free Printable Polynomial Zeros

1.

Factor to find the zeros:

5x^3-25x^2+30x

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2.

Factor. Find the zeros.

x^3+2x^2-4x-8

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3.

What does multiplicity tell you about the behavior of the graph at the zero x=-2 in the previous problem:

x^3\ +\ 2x^2-4x-8

a)

The graph crosses the x-axis at -2

b)

The graph has a turning point at -2

c)

It cannot be determined

4.

How many zeros in total should this function have?

x^3+x^2-x\ +\ 2

a)

0

b)

1

c)

2

d)

3

5.

$x^3+x^2-x\ +\ 2$
Graph the function in your calculator. Where do you see a zero?

a)

x = 2

b)

x = -2

c)

x = 1

d)

x = -1

6.

$x^3+x^2-x\ +\ 2$
Use the zero, x = -2, and do synthetic division.
What is the resulting quadratic?

a)

$x^2-x+1$

b)

$x^2+5x\ -24$

c)

$x^2\ +3x\ +\ 5$

d)

$x^2-2x\ +\ 2$

7.

Use quadratic formula to find the remaining zeros:

x^2-x+1

a)

$\frac{-1\pm i\sqrt{7}}{2}$

b)

$\frac{1\pm i\sqrt{3}}{2}$

c)

$\frac{-1\pm i\sqrt{5}}{2}$

d)

$\frac{1\pm i\sqrt{11}}{2}$

8.

What are the solutions to the inequality?

x^{3\ }-4x<0

a)

$\left(-\infty,\ -2\right)\left(0,\ 2\right)$

b)

$\left(-2,\ 0\right)\left(2,\ \infty\right)$

9.

a)

Even

b)

Odd

c)

Neither

10.

a)

Even

b)

Odd

c)

Neither

11.

a)

Even

b)

Odd

c)

Neither

12.

$f\left(x\right)\ =\ 7x^{3\ }-\ x$

a)

Even

b)

Odd

c)

Neither

13.

$g\left(x\right)=x^2-2x\ +\ 3$

a)

Even

b)

Odd

c)

Neither

14.

Use rational root theorem to list all the possible rational roots:

2x^3-3x^2+4x+10

a)

$\pm1,\pm2,\pm5,\pm10$

b)

$\pm1,\pm2$

c)

$\pm1,\pm2,\pm5,\pm10,\pm\frac{1}{2},\pm\frac{5}{2}$

d)

$\pm1,\pm\frac{1}{2},\pm\frac{1}{5},\pm\frac{1}{10},\pm2,\ \pm\frac{2}{5}$

15.

Find the polynomial function that has degree 2 and has a zero at (5+4i).

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Polynomial Zeros

Total questions: 15

Worksheet time: 38mins

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