Factoring

One Variable

100

2x+5x

x(2+5)

200

2x + 6

2(x + 3)

300

x² − 4x + 24

not factorable

400

-3x² + 12x ^_ 18

-3(x^{2 _} 4x + 6)

500

6x⁵ + 30x⁴ + 12x³

6x³(x² + 5x + 2)

Two Variables

100

10m+2x

2(5m+x)

200

y^{2 _} 2hy ^- 24h²

(y ^_  6h)(y +4h)

300

2x²−4x+xy−2y

(2x+y)(x−2)

400

3xy ^_ 24x^2 _ 7y + 56x

(y ^_ 8x)(3x ^_ 7)

500

3x^2 _ 13xy + 4y²

(3x ^_ y)(x ^_ 4y)

Grouping

100

m² + 2m − 24

(m+6)(m+4)

200

2p² + 2p − 4

2(p − 1)(p + 2)

300

6v² + 66v + 60

6(v+10)(v+1)

400

a^{3 _} 5a² + 6a ^_ 30

(a ^_ 5)(a² + 6)

500

5v^{3 _} 2v² + 25v ^_ 10

v²(5v ^_ 2) + 5(5v ^_ 2) or (5v  ^_ 2)(v² + 5)