Factoring Polynomials

Factoring GCF

100

2x + 6y - 10z

What is 2(x + 3y - 5z)

200

x³ + 5x² + 7x

What is x(x² + 5x + 7)

300

6x⁴ - 9x³ + 24x²

What is 3x²(2x² - 3x + 8)

400

2x(x + 5) + 7(x + 5)

What is (2x + 7)(x + 5)

500

x(x - 1) + y(x - 1) +z(x - 1)

What is (x + y + z)(x - 1)

Tougher Trinomials (ax^2 +bx+c ; a >1)

100

9x² +6x +1

What is (3x +1) (3x +1)

200

6x²+x-2

What is (2x-1)(3x+2)

300

9x²+12x+4

What is (3x+2)² or (3x+2)(3x+2)

400

8x² - 9x + 1

What is (8x - 1)(x - 1)

500

6x²-11x+4

What is (2x-1)(3x-4)

Difference of Squares

100

x² - 100

What is (x + 10)(x - 10)

200

25x² - 36

What is (5x + 6)(5x - 6)

300

100x² - 121y²

What is (10x + 11y)(10x - 11y)

400

x⁴ - 81 (This has two steps to complete the factoring.)

What is (x² + 9) ( x² -9) OR (x² +9) (x+3)(x-3)

500

16x⁴ - 1

What is (4x² + 1)(4x² -1) OR (4x² +1) (2x -1) (2x+1)

E-Z Trinomials (ax^2 +bx +c; a = 1)

100

x² + 10x +25

What is (x + 5) (x+5)

200

x² - 2x + 1

What is (x - 1) (x-1)

300

32 +18r +r²

What is (16 +r)(2+r)

400

x² - 10x - 24

What is (x -6) (x -4)

500

x² + 11x +30

What is (x + 5) (x+6)

Factoring by Grouping

100

2ax + 6xc +ba + 3bc

What is (2x +b)(a +3c)

200

6mx - 4m + 3rx -2r

What is (2m +r) ( 3x -2)

300

2x²+8x+3x+12

What is (x+4)(2x+3)

400

3ax - 6bx + 8b - 4a

What is (a-2b)(3x -4)

500

2x³ - 5xy² - 2x² y + 5y³

What is (2x² - 5y²) (x-y)