Factoring Polynomials

Factor by GCF

100

Factor the GCF:

2x²-4xy+6y

2x(x-2y+6y)

200

Factor the GCF:

25x⁵y-15y

5y(5x⁴-3)

300

Factor the GCF

2x-3y-7z+9

1(2x-3y-7z+9)

400

Factor the GCF

-4x⁴y³z² - 24xy³z +32x⁴y³z

-4xy³z(x³z + 6 - 8x³)

Factor a Trinomial

100

x²+4x+4

(x+2)(x+2)

200

x²+x-56

(x+8)(x-7)

300

-2x²-12x-16

-2(x²+6x+8)

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

400

x³-12x²+27x

x(x²-12x+27)

x(x-9)(x-3)

Factor Binomial

100

x²-1

(x+1)(x-1)

200

4x²-25

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

300

-81x²-121

-(81x²+121)

Cannot factors since it is not a difference of squares.

400

-144x²y⁴+25z⁹

-(144x²y⁴-25z⁹)

-(12xy² - 5z³)(12xy²+5z³)

Factor by Grouping

100

x³-2x²+2x-4

x²(x-2)+2(x-2)

(x²+2)(x-2)

200

5x³-4x²-25x+20

x²(5x-4)-5(5x+4)

(x²-5)(5x-4)

300

9x³-9x²-4x+4

9x²(x-1)-4(x-1)

(x-1)(9x^2-4)

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

400

x⁴+3x³-3x²-9x

x(x³+3x²-3x-9)

x(x²(x+3)-3(x+3))

x(x+3)(x²-3)

Solving Polynomials

100

3x-4x = 9

-x = 9

x = -9

200

9x²-3x = 0

3x(3x-1)=0

3x=0 or 3x - 1= 0

x=0, x= 1/3

300

x²-1x-56=0

(x-8)(x+7)=0

x-8=0, x+7=0

x=8, x=-7

400

16x³-4x²-36x+9=0

4x²(4x-1)-9(4x-1) =0

(4x²-9)(4x-1)=0

(2x-3)(2x+3)(4x-1)=0

x=2/3, x=-2/3, x=1/4

500

A rectangle has a length of x-5 feet and a width of x-2.  Find the dimensions of the rectangle given that the area is equal to 40.

A = (x-5)(x-2)

40 = x²-2x-5x+10

0 = x²-7x-30

0 = (x-10)(x+3)

x=10, x=-3

x=10, 

length: 10-5 =5. width: 10-2= 8