Factoring Polynomials Review

Random Factoring

100

The first step in all factoring

Look for and factor out the GCF

200

Factor Completely

y³+9y²

y²(y+9) 

300

Factor completely

x²+9x+20

(x+5)(x+4)

400

Factor Completely

2y²-16y+32

2(y-4)(y-4)

500

Factor Completely

4x³-25x²+6x

x(4x-1)(x-6)

600

Random:

Factor Completely

x^5-x^3+x^2-1

(x+1)(x+1)(x-1)(x²-x+1) 

Group Soup

100

True or False

To factor by grouping, you MUST group your terms in groups of 2 and look for a GCF for each group.

False

You can group them in groups bigger than 2 if necessary

200

Factor completely

12a³ − 9a² + 4a − 3

(3a² + 1)(4a − 3)

300

We use the grouping method to factor polynomials with how many terms?

4 or more terms

400

Factor completely

m³ − m² + 2m − 2

(m² + 2)(m − 1)

500

Factor Completely

15x³ + 5x² + 3x + 1

(5x²+1)(3x+1)

600

Factor Completely

2x³+20-8x-5x²

(x+2)(x-2)(2x-5)

Square Dancing

100

True or False

To factor something that qualifies as both a difference of squares AND a difference of cubes, factor as cubes first to get done more efficiently.

False

Binomials that are BOTH differences of squares and cubes should be factored as squares first. 

200

Factor Completely

4x²+9

PRIME

300

Factor Completely

36x² - 4y²

4(3x-y)(3x+y)

400

Factor Completely

75x³-3x

3x(5x+1)(5x-1)

500

Factor Completely

-81x²y²+49x⁴

x²(7x+9y)(7x-9y)

600

Factor completely

48x²-3

3(4x+1)(4x-1)

Accidental factoring

100

True or False

A trinomial with integer coefficients where a = 1 can always be factored into two binomials.

False - not all trinomials are factorable.  Some are prime

200

Factor Completely

10x³y³-15x³y³z+5x⁴y³-5x²y²

5x²y²(2xy-3xyz+x²y-1)

300

The three types of binomials that will factor (after taking out any GCF)

Difference of squares, Sum of two cubes, Difference of two cubes

400

Factor Completely

12x²-11x-15

(3x-5)(4x+3)

500

Factor Completely

27x²-66x+7

(9x-1)(3x-7)

600

Factor Completely

-16x²+48x-36

-4(2x-3)²

Ice Cubes

100

Factor Completely

(x + 2)³+(2x - 1)³

(3x + 1)(3x² - 3x + 7)

200

Factor completely

x³-64

(x-4)(x²+4x+16)

300

Factor Completely

8x³-125

(2x-5)(4x²+10x+25)

400

192x⁵+24x²

24x²(2x+1)(4x²-2x+1)

500

Factor Completely

x⁹+512

(x+2)(x²-2x+4)(x⁶-8x³+64)

600

Factor Completely

x⁶-64

(x+2)(x²-2x+4)(x-2)(x²+2x+4)

My Mama didn't raise no fool

100

Factor Completely

x³ + 1

(x + 1)(x²  - x + 1)

200

Factor Completely

y⁸-81

(y²+3)(y²-3)(y⁴+9)

300

Factor Completely

(x+4)²-(y+1)²

(x+y+4)(x-y+3)

400

Factor Completely

64x⁶ - 1

(2x-1)(2x+1)(4x²+2x+1)(4x²-2x+1)

500

Factor Completely

(x-1)²-10(x-1)+25

(x-6)²

600

Factor Completely

36x + 27 - (4x+3)³

(-4x)(4x+3)(4x+6)