~6.4: Factoring & Solving Polynomials Equations~

Difference of Cubes

100

Factor the polynomial: x^3-8

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

200

Factor the polynomial: 125x^3-8

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

300

Factor the polynomial: 16u5-250u2

2u²(2u-5)(4u²+10u+25)

400

Factor the polynomial: 32x³-4

4(2x-1)(4x²+2x+1)

500

Factor the polynomial: -3x³+192y³

-3(x-4y)(x²+4xy+16y²)

Sum of Two Cubes

100

Factor the polynomial: x³+64

(x+4)(x²-4x+16)

200

2x³+54

2(x+3)(x²-3x+9)

300

Factor the polynomial: 27x³+216

(3x+6)(9x²-18x+36)

400

Factor the polynomial: 216x³+1

(6x+1)(36x²-6x+1)

500

Factor the polynomial: 1,000x³+27

(10x+3)(100x²-30x+9)

Factoring By Grouping

100

Factor by grouping: x³+x³+x+1

(x+1)(x²+1)

200

Factor by grouping: x³+3x²+10x+30

(x+3)(x²+10)

300

Factor by grouping: 2x³-5x²+18x-45

(2x-5)(x²+9)

400

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

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

500

Factor by grouping: 3x³-2x³-9x+6

(3x-2)(x²-3)

Factor Polynomials in Quadratic Form

100

FACTOR IT: 81x⁴-16

(9x²+4)(9x²-4)

Answer: (9x²+4)(3x+2)(3x-2)

200

FACTOR IT: 81-16x⁴

(9+4x²)(9-4x²)

Answer: (9+4x²)(3+2x)(3-2x)

300

FACTOR IT: m⁶-16m³+64

(m³-8)(m³-8)

Answer: (m-2)²(m²+2m+4)²

400

FACTOR IT: x⁴-40x²+144

(x²-36)(x²-4)

Answer: (x+6)(x-6)(x-2)(x+2)

500

FACTOR IT: 7x⁴-20x²+12

7x⁴-14x²-6x²+12

Answer: (7x²-6)(x²-2)

Solve Polynomial Equations

100

Solve: 2x³-6x²=0

Answers: 0 and 3

200

Solve: x³+27=0

(Only solve for real roots)

Answer: 3

300

Solve: a³-9a²+14a

Answer(s): 0, 7, 2

400

Solve 4x³-2x²=36x-18

3, -3, 1/2

500

36x=40x²-4x³

0, 1, 9