Factoring

Grouping

100

x²+3x+2x+6

(x+2)(x+3)

200

12x³+2x²-30x-5

(2x²-5)(6x+1)

300

25v³+5v²+30v+6

(5v²+6)(5v+1)

400

63n³+54n²-105n-90

3(3n²-5)(7n+6)

500

-75n+105n³-125+175n²

5(7n²-5)(3n+5)

Sum and Product

100

x²+5x+4

(x+4)(x+1)

200

x²+16x+55

(x+5)(x+11)

300

x²-16x+60

(x-6)(x-10)

400

5n²+19n+12

(5n+4)(n+3)

500

4x²-35x+49

(x-7)(4x-7)

Quadratic Formula

100

b²-4b+4

(x-2)

200

2x²+2x-12

x=2, x=-3

2(x-2)(x+3)

300

4b²+8b+7=4

4(x+1/2)(x+3/2)

2x2(x+1/2)(x+3/2)

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

400

2x²-36=x

2(x-9/2)(x+4)

(2x-9)(x+4)

500

5x²=80

x=4, x=-4

5(x-4)(x+4)

Random

100

a²+6a+8

(x+4)(x+2)

200

x²+14x=51

x=3, x=-17

(x-3)(x+17)

300

5k²=60-20k

x=2 , x=-6

5(x-2)(x+6)

400

2x²-18

2(x-3)(x+3)

500

6x²+x-2

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

Difference of Squares

100

x²-y²

(x-y)(x+y)

200

d²-16p²

(d-4p)(d+4p)

300

81d²-64

(9d-8)(9d+8)

400

36h²-100b⁸

(6h+10b⁴)(6h-10b⁴)

500

49x²-(y+6)²

(7x-(y+6))(7x+(y+6)) = (7x-y-6)(7x+y+6)