FACTORING POLYNOMIALS

Factoring trinomials

100

Factor into two binomials: x²+8x+12

(x+6)(x+2)

200

Factor into two binomials: m²-11m+18

(m-9)(m-2)

300

Factor into two binomials: x²+5x-24

(x+8)(x-3)

400

Factor into two binomials: y²-6y-7

(y-7)(y+1)

500

Factor into two binomials: x²-x-56

(x-8)(x+7)

Factoring Trinomials- harder

100

Factor into two binomials: 2x²+7x+3

(2x+1)(x+3)

200

Factor into two binomials: 5n²+26n+5

(5n+1)(n+5)

300

Factor into two binomials: 3x²-10x+7

(3x-7)(x-1)

400

Factor into two binomials: 7x²-36x+5

(7x-1)(x-5)

500

Factor into two binomials: 2x²-12x+10

(2x-2)(x-5)

Finding the GCF

100

Find the GCF: 3x², 12x

3x

200

Find the GCF: 4x³, 10x²

2x²

300

Find the GCF: 2x⁵, 9x⁴

x⁴

400

Find the GCF: 18x³, 32x²+6x

2x

500

Find the GCF: 12m⁴n³, 6m³n², 24m²n⁴

6m²n²

Factor by GCF

100

Factor by GCF: 14n²+10n

2n(7n+5)

200

Factor by GCF: 18x³-6x

6x(3x²-1)

300

Factor by GCF: 8-4a²

4(2-a²)

400

Factor by GCF: 4x⁴+16x³-8x²

4x²(x²+4x-2)

500

Factor by GCF: 10a³b⁴-6a²b⁶

2a²b⁴(5a³-3b²)

Types of Factoring

100

What are the main steps for finding a GCF?

-Find the GCF of the coefficient

-Find the most amount of variables you can take out

200

What are the main steps of "basic factoring"?

-Find two numbers that multiply to C and add to B.

-Express your answer in factored form.

300

What are the main steps for the diamond/box method?

-Make the diamond with ac on the top and b on the bottom?

-Find two numbers that multiply to ac and add to b

-Fill out the box

-Find factors that correctly multiply to the numbers in the box

-Express your answer in factored form

400

What are the main steps for Slide and Divide?

-Slide A over to C and multiply

-Factor what remains normally

-Divide each number by the original A term
(Simplify the fraction if necessary!)

-Slide the denominator in front of your variable in factored form

500

What are the main steps of factoring if all three numbers are divisible by a number?

-Find the GCF of all of the coefficients

-Divide each term by that number

-Factor what remains

-Express your answer in factored form with the number you factored out.