All Methods of Factoring

Factoring Binomials

100

2x²+14x

2x(x+7)

200

4x³+12x

4x(x²+3)

300

25n³+5n²

5n(5n²+n)

400

4x+2xy

2x(2+y)

500

3x²+3xy

3x(x+y)

Factoring Polynomials when a = 1

100

n²+4n-12

(n-2)(n+6)

200

m²+m-90

(m-9)(m+10)

300

k²-13k+40

(k-5)(k-8)

400

x²+22x+121

(x+11)(x+11) or (x+11)²

500

x²+3x-54

(x+9)(x-6)

Factor by GCF

100

2x²-12x+16

2(x-4)(x-2)

200

4x²+44x+40

4(x+10)(x+1)

300

6x²-6x-72

6(x+3)(x-4)

400

5x²-50x+125

5(x-5)(x-5) or 5(x-5)²

500

3x²+45x+108

3(x+12)(x+3)

Factor by Grouping

100

2n²+5n+2

(2n+1)(n+2)

200

6x²+37x+6

(x+6)(6x+1)

300

6n²+5n-6

(2n+3)(3n-2)

400

5x²-18x+9

(5x-3)(x-3)

500

6x²+7x-49

(3x-7)(2x+7)

Regents Questions

100

Which trinomial is written in standard form and has a constant term of five?

(1) x⁵-4x²+10

(2) 2x²+6x⁴+5

(3) 5x⁴-3x²+1

(4) 4x⁵-8x²+5

(4) 4x⁵-8x²+5

200

The expression x²-26x-120 is equivalent to

(1) (x+4)(x-30)

(2) (x-4)(x+30)

(3) (x-20)(x+6)

(4) (x+20)(x-6)

(1) (x+4)(x-30)

300

Use the quadratic formula to solve 2x²-4x-3=0, round to the nearest thousandth.

x = 2.581

x = -0.581

400

Which equation is equivalent to x²-6x=27?

(1) (x-3)²=27-9

(2) (x-3)²=27+9

(3) (x-3)²=27+36

(4) (x-3)²=27-36

(2) (x-3)²=27+9

500

Using the method of completing the square, express x²+14x-28=0 in the form (x-p)²=q.

(x+7)²=77