Multiplying/Dividing Polynomials

FOIL

100

(x+1)(x+2)

x²+3x+2

200

(x-2)²

x²-4x+4

300

(2x+8)(3x-12)

6x²-96

400

(xy+x)(xy+y)

x²y²+x²y+xy²+xy

500

(4x²-7xy)(5x²+xy)

20x⁴-31x³y-7x²y²

Box Method

100

(x+2)(x+3)

x²+5x+6

200

(3x+6)(x-2)

3x²-12

300

(2x+2)(3x²-4x+5)

6x³-2x²+2x+10

400

(x-1)(3x²+3x-3)

3x³-6x+3

500

(x⁵+4x³-x)(2x⁴+2x³-2x)

2x⁹+2x⁸+8x⁷+6x⁶-2x⁵-10x⁴+2x²

Each-to-Each

100

(x-1)(x+2)

x²+x-2

200

(-x+1)(x-3)

-x²+4x-3

300

(4x-3)(2x²-x-1)

8x³-10x²-x+3

400

(3x+2)(9x²-6x+4)

27x³+8

500

(x+y+z)(x²y+xy²+yz)

x³y+2x²y²+xyz+xy³+y²z+x²yz+xy²z+yz²

Reverse Box

100

(x²-6x+9)÷(x-3)

x-3

200

(2x²+7x+3)÷(x+3)

2x+1

300

(x⁴+2x³+2x²+2x+1)÷(x+1)

x³+x²+x+1

400

(x³+2x²-1)÷(x+1)

x²+x-1

500

(2x⁶-3x⁵-x⁴-2x²+3x+1) ÷ (2x²-3x-1)

x⁴-1

Long Division

100

(x²+14x+40)÷(x+4)

x+10

200

(x³+13x²+46x+24)÷(x+6)

x²+7x+4

300

(8x³+65x²+62x-7)÷(x+7)

8x²+9x-1

400

(x³-4x²+3)÷(x-1)

x²-3x-3

500

(6x⁵+4x⁴-6x³+14x²-8) ÷ (6x+4)

x⁴-x²+3x-2