Factoring and Solving Jeopardy

Greatest Common Factor

100

Factor. 

2x² + 14

2(x² + 7)

200

Factor. 

8a - 16

8(a - 2)

300

Factor. 

25z² - 125xz

25z

400

Factor. 

9x²y - 45xy +9yz

9y(x² - 5x+ z)

500

Factor. 

-24x⁴y⁷+ 12x³y⁵-48x²y³   

-12x²y³(2x²y⁴ - xy² + 4) 

Trinomials

100

To factor the trinomial x²+8x+16 you find two numbers that add to 8 but multiply to this...

16

200

Factor.
x² + 8x + 12 

(x + 2)(x + 6)

300

Factor. 

x² - 6x + 8

(x - 4)(x - 2)

400

Factor. 

a²-8a+16.

(a-4)(a-4)

500

Factor. 

x²-11x+30

(x-6)(x-5)

TrinomialsA > 1

100

Factor.
3x² + 20x + 12

(3x+2)(x+6)

200

Factor.
3x² - 19x - 14 

(3x + 2)(x - 7)

300

Factor. 

4x² + 24x + 32

4(x + 2)(x + 4)

400

Factor. 

8x² + 18x + 9

(4x + 3)(2x + 3)

500

Factor. 

16x² - 8x + 1

(4x - 1)²

Difference of Squares

100

This is the first step of factoring ALWAYS...

Look for a GCF

200

Factor.
x² - 25

(x - 5)(x + 5)

300

Factor.
2x² - 200

2(x - 10)(x + 10)

400

Factor.
81x⁸ - 1

(9x⁴+1)(3x²-1)(3x²+1)

500

Factor 

64x²-81

(8x+9)(8x-9)

Solving

100

Solve. 

(x+3)(x-2)=0

x=-3 and x=2

200

Solve. 

2x(2x+1)(x-2)=0

x=0, x=-1/2, x=2

300

Solve. 

3(x²-9)(4x+7)=0

X=3, X=-3, X=-7/4

400

Solve. 

41x²-117x-105=-x^2

x=7/2 and x=-5/7

500

Solve.

8=-50m²-40m+2

x=-3/5 and x=-1/5

More Solving

100

Solve x²+7x+10 = 0

What is {-5, -2}?

200

Solve. 3x^2-15x = -18

x=2 and x=3

300

Solve 2x²-20 = -3x

x=-4 and x=5/2

400

Solve. 6x²+15 = 19x

x= 3/2 and x=5/3

500

Solve 7x²=28x

x=4 and x=0

Grouping

100

Factor.

8r^3-64r^2+r-8

(8r^2 + 1)(r - 8)

200

Factor

12p^3-21p^2+28p-49

(3p^2 + 7)(4p - 7)

300

Factor. 

63n³+54n²-105n-90

3(3n^2-5)(7n+6)

400

Factor. 2x³+3x²-18x-27

(x+3)(x-3)(2x+3)

500

Solve.

x^3+x^2-4x-4 = 0

{-2, -1, 2}