Polynomial Operations and Factoring

Polynomial Operations

100

Simplify 3x²+2x-4+x²+3x+2

4x²+5x-2

200

Subtract (4x²+6x+3)-(2x²+3x-2)

2x²+3x+5

300

Multiply (2x+5)(3x+4)

6x²+23x+20

400

Multiply (-8x²-2x+9)(6x-2)

-48x³+4x²+58x-18

500

The length of a rectangle is (6x+2) and the width is (2x-3). Write and simplify an expression for the perimeter of the rectangle. 

2(6x+2) + 2(2x-3)

16x-2

GCF

100

Find the GCF of 12x⁴+16x³

4x³

200

Factor 6x-3

3(2x-1)

300

Factor 4x²+12x

4x(x+3)

400

Factor 18x²y-45xy²+9y³z

9y(2x²-5xy+y²z)

500

A school is designing two rectangular garden sections with areas 18x³+30x² and 24x³+40x². Factor both expressions.

6x²(3x+5) and 8x²(3x+5)

Trinomials (a=1)

100

Factor x²+6x+8

(x+2)(x+4)

200

Factor x²-10x-24

(x+2)(x-12)

300

Factor p²+7p-30

(p-3)(p+10)

400

Factor k²-13k+40

(k-5)(k-8)

500

A rectangular patio has an area of x²-7x+12 square feet. What are its dimensions?

(x-3) ft by (x-4) ft

Trinomials (a≠1)

100

Factor 3x²-14x-5

(3x+1)(x-5)

200

Factor 2n²-11n+15

(2n-5)(n-3)

300

Factor 9y² - 6y + 1

(3y - 1)²

400

Factor 2x²+14x+3

Prime

500

Factor 4a²+ 6a - 40

2(2a-5)(a+4)

Other

100

x³+4x²-5x-20

(x²-5)(x+4)

200

Factor 4k³ - 7k² - 12k +21

(k²-3)(4k-7)

300

Factor x²-25

(x+5)(x-5)

400

Factor 4x³-14x²+6x

2x(2x-1)(x-3)

500

Factor 16x²-36

4(2x-3)(2x+3)