Free Printable Polynomial Roots and Factors Test Review

1.

The degree of the function is...

a)

the size of it

b)

the number of terms

c)

the greatest exponent on the variable

d)

How hot the function is

2.

What is the degree of $f\left(x\right)=\left(x+3\right)\left(x^2-4\right)$ ?

a)

3

b)

4

c)

1

d)

2

3.

Use the Fundamental Theorem of Algebra to determine the total number of REAL and IMAGINARY roots

$f\left(x\right)=x^8-17x^4+10x$

a)

4

b)

3

c)

8

d)

27

4.

Use the Fundamental Theorem of Algebra to determine the total number of REAL and IMAGINARY roots

$f\left(x\right)=8x^6+5x^2+23$

a)

6

b)

8

c)

23

d)

4

5.

Find the roots of the function: $f\left(x\right)=x\left(x+5\right)\left(x-7\right)$

$x=\$ type roots in the order of the problem above

(a)

6.

Find the roots of the function: $f\left(x\right)=x\left(2x-3\right)\left(5x-4\right)$

a)

$x=\frac{3}{2},\ \frac{4}{5}$

b)

$x=0,-\frac{3}{2},\ -\frac{4}{5}$

c)

$x=-\frac{3}{2},\ -\frac{4}{5}$

d)

$x=0,\frac{3}{2},\ \frac{4}{5}$

7.

Find the roots of the function: $f\left(x\right)=4x^3-5x^2-6x$

a)

$x=-\frac{3}{4},\ 2$

b)

$x=0,-\frac{3}{4},\ 2$

c)

$x=\frac{3}{4},-\ 2$

d)

$x=0,\frac{3}{4},\ -2$

8.

Find the roots of the function: $f\left(x\right)=4x^3+8x^2-9x-18$

a)

$x=-\frac{3}{2},\frac{3}{2},-\ 2$

b)

$x=-\frac{3}{2},\frac{3}{2},\ 2$

c)

$x=-\frac{2}{3},\frac{2}{3},-\ 2$

d)

$x=-\frac{2}{3},\frac{2}{3},\ 2$

9.

Find all of the factors and roots for the following function:

$\left(x+3\right)$ is a factor of the function $f\left(x\right)=3x^3+14x^2+13x-6$

a)

$x=-3,2,3$

b)

$x=x=-3,-2,-\frac{1}{3}$

c)

$x=-3,-2,3$

d)

$x=-3,-2,\frac{1}{3}$

10.

Write a polynomial function with a leading coefficient of -5 and roots of 3, -4 and 7

Factored Form

$f\left(x\right)=$ write your answer in order of the given information

(a)

11.

Write a polynomial function with a leading coefficient of -5 and roots of 3, -4 and 7

Standard Form

a)

$f\left(x\right)=x^3-6x^2-19x+84$

b)

$f\left(x\right)=-5x^3+30x^2+95x-420$

c)

$f\left(x\right)=-5x^3-6x^2-19x+84$

d)

$f\left(x\right)=x^2-3x-28$

12.

Write a polynomial function with a leading coefficient of 2 and roots of -3, 7i

Factored Form

a)

$f\left(x\right)=2\left(x+3\right)\left(x-7i\right)$

b)

$f\left(x\right)=2\left(x-3\right)\left(x-7i\right)$

c)

$f\left(x\right)=2\left(x+3\right)\left(x-7i\right)\left(x+7i\right)$

d)

$f\left(x\right)=2\left(x-3\right)\left(x-7i\right)\left(x+7i\right)$

Polynomial Roots and Factors Test Review

Total questions: 12

Worksheet time: 9mins

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