Factoring & Solving Polynomials Equations

Difference of Cubes

100

Factor the polynomial: u^3 - 216

Answer: (u + 6)(u^2 + 6u + 36)

200

Factor the polynomial: x^3-8

Answer: (x-2)(2x^2+2x+4)

300

Factor the polynomial: 125x^3-8

Answer: (5x-2)(25x^2+10x+4)

400

Factor the polynomial: x^4-27x

x(x - 3)(x^2 + 3x + 9)

500

Factor the polynomial: x^3- 1000

Answer: (x-10)(x^2+10x+100)

Sum of Two Cubes

100

Factor the polynomial: x^3+64

Answer: (x+4)(x^2-4x+16)

200

Factor the polynomial: x^3+27

Answer: (x+3)(x^2-3x+9)

300

Factor the polynomial: 27x^3+216

Answer: (3x+6)(9x^2-18x+36)

400

Factor the polynomial: 216x^3+1

Answer: (6x+1)(36x^2-6x+1)

500

Factor the polynomial: x^3+1000

Answer: (x+10)(x^2 - 10x + 100) 

Factoring By Grouping

100

Factor by grouping: (x^3+x^2+x+1)

Answer:(x+1)(x^2+1)

200

Factor by grouping: x^3+3x^2+10x+30

Answer: (x+3)(x^2+10)

300

Factor by grouping: 2x^3-5x^2+18-45

Answer: (2x-5)(x^2+9)

400

Factor by grouping: 3x^3-6x^2+x-2

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

500

Factor by grouping: 3x^3-2x^2-9x+6

Answer: (3x-2)(x^2-3)

Polynomial Long Division

200

6x^2 - 5x + 9) / (2x - 1) 

3x - 1 r 8 

300

(7x^3 + 11x^2 + 7x + 5) / (x^2 + 1)

Answer: 7x + 11 r -6

400

(3x^3 + 11x^2 + 4x + 1) / (x^2 + x)

3x + 8 r -4x + 1

500

(5x^4 - 2x^3 - 7x^2 - 39) / (x^2 + 2x - 4) 

Answer: 5x^2 - 12x + 37 r -122x + 109

Synthetic Division

100

(2x^2 - 7x + 10) / (x - 5) 

Answer: 2x + 3 r 25

200

(x^3 - 4x + 6) / (x + 3)

Answer: x^2 - 3x + 5 r -9

300

(4x^2 - 13x - 5) / (x - 2) 

Answer: 4x - 5 r -15

400

(x^4 - 5x^3 - 8x^2 + 13x - 12) / (x - 6)

Answer: x^3 + x^2 - 2x + 1 r -6

500

(2x^5 + x) / (x + 4) 

Answer: 2x^4 - 8x^3 + 32x^2 - 128x + 513 r -2052