Factoring Jeopardy!

Binomials

100

Factor completely: m³ + 27

(m + 3)(m² - 3m + 9)

200

Factor completely: 2x⁴ - 54x

2x(x - 3)(x² + 3x + 9)

300

Factor completely: 28n² - 7

7(2n + 1)(2n - 1)

400

Factor completely: 864rx⁶ + 1372ry⁶

4r(6x² + 7y²)(36x⁴ - 42x²y² + 49y²)

500

Factor completely: 64x⁶ - y⁶

(2x + y)(2x - y)(4x² + 2xy + y²)(4x² - 2xy + y²)

Trinomials

100

Factor completely: n² + 2n +1

(n + 1)²

200

Factor completely: 3x⁵ + 35x³ + 72x

x(3x² + 8)(x² + 9)

300

Factor completely: -40x² + 244xy - 24y²

-4(x - 6y)(10x - y)

400

Factor completely: x⁸ + x⁴ - 90

(x⁴ + 10)(x² + 3)(x² - 3)

500

Factor completely: 832x² + 1456xy + 637y²

13(8x + 7y)²

4-Term Polynomials

100

Factor completely:8xy + 3x + 48y + 18

(x + 6)(8y + 3)

200

Factor completely: 2n³ + 4n² + n + 2

(2n² + 1)(n + 2)

300

Factor completely: 240ab + 40a² - 150b - 25a

5(8a - 5)(6b + a)

400

Factor completely: 16x³y³ - 120x²y²p² + 96x³y²p - 20x²y³p

4x²y²(4x - 5p)(y + 6p)

500

Factor completely: 2040y³x - 2850y²v⁴ + 1200y²xv³ - 4845y³v

15y²(8x - 19v)(17y + 10v³)

Higher Order Polynomials

100

Identify the rational zeros of f(x)= x² - 6x + 5. Identify the multiplicity of the root/s (single, double, etc.)

Two rational zeros at x=1 and x=5 (both single roots)

200

Find the rational zeros of f(x)= x⁴ + 6x³ + 25x². Identify the multiplicity of the root/s (single, double, etc.)

One rational zero at x=0 (double root)

300

Find the rational zeros of f(x)= -4x⁴ - 20x³ - 35x² - 21x. Identify the multiplicity of the root/s (single, double, etc.)

Two rational zeros at x=0 and x=-1.5 (both single roots)

400

For the function f(x)= 3x⁴ - 14x² + 8, 

1. find the rational roots

2. use synthetic division to factor into linear and irreducible quadratic factors

1. rational zeros at x=-2 and x=2

2. f(x)= (x - 2)(x + 2)(3x² - 2)

500

For the function f(x)= 3x⁴ + 5x³ + 12x² + 20x, 

1. find the rational roots

2. use synthetic division to factor into linear and irreducible quadratic factors

1. rational roots at x=0 and x=-5/3

2. f(x)= x(3x + 5)(x² + 4)

GCF

100

Find the GCF of: 13a + 20b

GCF = 1

200

Find the GCF of: 8x² + 10x

GCF = 2x

300

Find the GCF of: -15d⁵ + 45d³ - 60d²

GCF = -15d² or 15d²

400

Find the GCF of: 315mn² - 504m²n - 588mn⁴

GCF = 21mn

500

Find the GCF of: 8113a³c² + 2394ac³ + 23674acb² + 15295acb

GCF = 133ac