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: 8x^3-8

Answer: (2x-2)(4x^2+6x+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: 125a^3 + 8b^2

Answer: (5a + 2b)(25a^2 - 10ab + 4b^2)

Sum of Two Cubes

100

Factor the polynomial: x^3+64

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

200

Factor the polynomial: 2x^3+54

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: 1,000x^3+27

Answer: (10x+3)(100x^2-30x+9)

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: 35xy - 5x - 56y + 8

(5x - 8)(7y - 1)

500

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

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

Polynomial Long Division

400

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

3x + 8 r 4x + 1

500

(7x^3 + 11x^2 + 7x + 5) / (x^2 + 1) 

Answer: 7x + 11 r -6

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^3 - 8x^2 + 32x - 127 r 512