Free Printable Unit 7 Lesson 7: Solving Polynomial Equations

1.

Factor using the greatest common factor.
$18x^3y^4+12x^2y^3-6xy^2$

a)

$6xy^2\left(3x^2y^2+2xy-1\right)$

b)

$6xy\left(3x^2y^3+2xy^2-y\right)$

c)

$6\left(3x^3Y^4+2x^2y^3-xy^2\right)$

d)

$6xy^2\left(3x^2y^2+2xy\right)$

2.

Factor using the greatest common factor.
$4x^5y-10x^3y^6+8x^4y^2$

a)

$2x^3y\left(2x^2-5y^5+4xy\right)$

b)

$x^3y\left(4x^2-10y^5+8xy\right)$

c)

$2\left(2x^5y-5x^3y^6+4x^4y^2\right)$

d)

$2xy\left(2x^4-5x^2y^5+4x^3y\right)$

3.

Factor.
$x^4-4x^2-5$

a)

$\left(x^2+7\right)\left(x^2-2\right)$

b)

$\left(x^2-7\right)\left(x^2+2\right)$

c)

$\left(x^2-7\right)\left(x^2-2\right)$

d)

$\left(x^2+7\right)\left(x^2+2\right)$

4.

Factor using difference of cubes.
$x^3-8$

a)

$\left(x-2\right)\left(x^2+2x+4\right)$

b)

$\left(x-2\right)\left(x^2+2x+2\right)$

c)

$\left(x+2\right)\left(x^2-2x+4\right)$

d)

$\left(x+2\right)\left(x^2-2x+2\right)$

5.

Factor.
$x^4-4x^2-5$

a)

$\left(x^2-5\right)\left(x^2+1\right)$

b)

$\left(x^2+5\right)\left(x^2-1\right)$

c)

$\left(x^2-5\right)\left(x^2-1\right)$

d)

$\left(x-5\right)\left(x+1\right)$

6.

Factor using the sum of cubes.
$27x^3+1$

a)

$\left(3x+1\right)\left(9x^2-3x+1\right)$

b)

$\left(3x+1\right)\left(3x^2-3x+1\right)$

c)

$\left(3x-1\right)\left(3x^2+3x+1\right)$

d)

$\left(3x-1\right)\left(9x^2-3x+1\right)$

7.

Factor completely.
$x^4-13x^2+36$

a)

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

b)

$\left(x^2-4\right)\left(x^2-9\right)$

c)

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

d)

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

8.

Factor using difference of cubes.
$8x^3-125$

a)

$\left(2x-5\right)\left(4x^2+10x+25\right)$

b)

$\left(2x-5\right)\left(2x^2+10x+25\right)$

c)

$\left(2x+5\right)\left(4x^2-10x+25\right)$

d)

$\left(2x+5\right)\left(2x^2-10x+25\right)$

9.

Solve the equation by factoring.
$x^4-29x+100=0$

a)

$x=5,-5,2,-2$

b)

$x=5,2$

c)

$x=-5,-2$

d)

$x=25,4$

10.

Solve the equation by factoring.
$x^4-25x^2+144=0$

a)

$x=3,-3,4,-4$

b)

$x=3,4$

c)

$x=-3,-4$

d)

$x=9,16$

11.

Solve the equation by factoring.
$x^3-49x=0$

a)

$x=0,7,-7$

b)

$x=7,-7$

c)

$x=0,7$

d)

$x=0,49$

12.

Solve the equation by factoring.
$x^4-15x^2-16=0$

a)

$x=1,-1,4,-4$

b)

$x=1,4$

c)

$x=-1,-4$

d)

$x=1,16$

Unit 7 Lesson 7: Solving Polynomial Equations

Total questions: 12

Worksheet time: 36mins

Similar Resources on Wayground