Free Printable Factors of Polynomial Functions

1.

Given $\left(x+1\right)$ is a factor of the polynomial $f\left(x\right)\ =\ 4x^3-12x^2-x+15$

use synthetic division to help you find
all of the other factors.
Choose ALL that apply.

a)

$\left(2x-5\right)$

b)

$\left(2x+3\right)$

c)

$\left(2x-3\right)$

d)

$\left(2x+5\right)$

2.

Write the cubic polynomial in factored form with
zeros -1, 1, and 4

a)

(x + 1) (x - 1) (x - 4)

b)

x³ - 4x² - x + 4

c)

(x + 1) (x - 1) (x + 4)

d)

x³ - 4x² - x - 4

3.

Factor and solve:
0=x³+11x²+24x

a)

x=8,3

b)

x=-8,-3

c)

x=-8,-3,0

d)

x=0, 8, -3

4.

Given $\left(x-1\right)$ is a factor of the polynomial $f\left(x\right)=x^3-7x^2-x+7$

use synthetic division to rewrite the polynomial in factored form.

$f\left(x\right)=$

a)

$\left(x-1\right)\left(x-7\right)\left(x+1\right)$

b)

$\left(x-1\right)\left(x+7\right)\left(x-1\right)$

c)

$\left(x-1\right)\left(x-6\right)\left(x-1\right)$

d)

$\left(x-1\right)\left(x-6\right)\left(x+1\right)$

5.

Which standard form function matches the factored form:
y = (x + 1)(x - 3)

a)

y = x² + x - 3

b)

y = x - 2

c)

y = x² - 2x - 2

d)

y = x² - 2x - 3

6.

Which standard form function matches the factored form:
y = (x + 1)(x - 1)(x + 4)

a)

y = x³ - x² - 4x

b)

y = x³ + 4x² - x - 4

c)

y = x³ - 4x² + x + 4

d)

y = x³ + x² - x - 4

7.

x²- 16

a)

( x - 4) ( x - 4)

b)

( x - 4) ( x + 4)

c)

( x - 8) ( x + 8)

8.

3x²- 75

a)

3( x + 5 ) ( x - 5 )

b)

3( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x - 5 )

9.

Factor f(x)= x³ - 2x²-13x - 10 given that (x - 5) is one factor.

a)

(x- 5)(x - 1)(x - 2)

b)

(x - 5)(x + 2)(x - 2)

c)

(x - 5)(x + 2) (x + 1)

d)

(x - 5)(2x - 13)

10.

Find all zeros:
ƒ(x) = x(4x - 3)(x + 2)

a)

x = 0, ¾, 2

b)

x = 0, -¾, -2

c)

x = 0, 3, -2

d)

x = 0, ¾, -2

Factors of Polynomial Functions

Total questions: 10

Worksheet time: 10mins

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