Quadratics: Factoring and Solving

When a=1

100

Factors of 

x²+9x+8

(x+8)(x+1)

200

Factors of 

x²+x-90

(x+10)(x-9)

300

Factors of 2x²+34x+140

2(x+10)(x+7)

400

Factors of 5k²+30k-200

5(k-4)(k+10)

500

Factors of 

6n²-12n-378

6(n+7)(n-9)

Special Products

100

Factors of 

x²-4

(x+2)(x-2)

200

Factors of 

25x²-9

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

300

Factors of 

25x²+20x+4

(5x+2)²

400

Factors of 

75p²-30p+3

3(5p-1)²

500

Factors of

18x²+32

Not factorable!

When a>1

100

Factors of 

2x²+x-6

(2x-3)(x+2)

200

Factors of 

2b²+15b+27

(2b+9)(b+3)

300

Factors of 

2x²-5x

x(2x-5)

400

Factors of 

10x²+56x-24

2(5x-2)(x+6)

500

Factors of

20k²+72k-140

4(5k-7)(k+5)

Solve by factoring

100

Solve

x²-10x+24=0

{4,6}

200

Solve

n²=-4n+32

{4,-8}

300

Solve

m²+6m=0

{-6,0}

400

Solve

5x²-24=14x

{-6/5,4}

500

Solve

7m²-35=44m

{-5/7,7}

Short Answer

100

What is a GCF?

Greatest Common Factor - what every term can be divided by

200

What is the first step in factoring?

GCF!

300

How can we tell that a quadratic is a difference of squares?

If both terms are perfect squares and they are being subtracted

400

When solving by factoring, how do we find solutions from our factors?

Set each factor equal to zero and solve / flip the sign

500

When do we have to use the long method of factoring? 

When a>1