Get Ready to Factor!

Common Factoring

100

Is it possible to factor:

7x+5

No.

200

Common Factor: 

3x+6y

3(x+2y)

300

Common Factor: 

45a²b−60ab²

15ab(3a-4b)

400

Common Factor: 

5x(x+3)+(x+3)

(x+3)(5x+1)

500

Common Factor:

 20(x+1)-15x²(x+1)+10y(x+1)

(x+1)(4-3x²+2y)

Factor by Grouping

100

Factor by Grouping: 

2x³+4x²+3x+6

(2x²+3)(x+2)

200

Factor by Grouping: 

a³+2a²+a+2

(a+2)(a²+1)

300

Factor by Grouping:

2x³+7x²+4x+14

(2x+7)(x²+2)

400

Factor by Grouping: 

x³+5x²-2x-10

(x²-2)(x+5)

500

Factor by Grouping:

6x²-3x+4x-2

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

Identify the Factoring Mistake

100

x²+7x+10=(x+10)(x+1)

They should add up to 7, not 11.

(x+2)(x+5)  

200

4x³+8x²=4x(x³+2x²)

The GCF is 4x², not 4x.

4x²(x+2)  

300

5x⁴+10x²=5x²(x³+2)

Incorrect exponents when dividing by the GCF.

x⁴ ÷ x² = x², not x³ 

400

3x²-9x-30=(x-15)(x+6)

Forgot to factor out GCF (3) before applying MAN method.

3(x² - 3x - 10) = 3(x+2)(x-5)

500

3x³−6x²+2x−4=3x²(x−2x)+2(x−2)

They subtracted an extra x instead of factoring the correct GCF.

3x²(x−2)+2(x−2)  

Type 1 Factoring (MAN Method)

100

Factor:

x²+5x+6

(x+2)(x+3)

200

Factor:

x²+8x+15

(x+5)(x+3)

300

Factor:

3x²+3x-36

3(x+4)(x-3)

400

Factor:

x²+2x-24

(x+6)(x-4)

500

Factor:

3x²-39x+126

3(x-6)(x-7)

General Trivia

100

Before choosing a way to factor, you should first check for a... (hint; think about a three letter acronym)

GCF.

200

What is the purpose of factoring?

It finds the x-intercepts of an equation.

300

What method would you use to factor this expression:

ax + 3x + ay +3y

Factor by Grouping.

400

What are three other names for x-intercepts?

Roots, zeros, solutions.

500

Which of these expressions cannot be factored any further?

A) x²+5x+6x  OR  B) x²+2x+5x

B) x²+2x+5x