Factoring Polynomials (Roupas)

A

1

2x² + 10x - 16

2(x² + 5x - 8) 

2

9x² -1

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

3

 x³ + x² + x

x(x² + x + 1)

4

1 - 4x²

(1 + 2x)(1 - 2x) 

5

8x²y −12x³y²

4x²y(2 - 3xy) 

B

1

x² + 13x + 12

(x+12)(x+1) 

2

 2x⁴ - 16x³ + 2x

2x(x³ - 8x² + 1) 

3

 2x² + 8x − 90

2(x+9)(x-5)

4

x² − 13x + 36

(x-9)(x-4)

5

x² − 20x − 125

(x-25)(x+5) 

C

1

36x²-1

(6x + 1)(6x -1)

2

2x² + 2x - 4

2(x+2)(x-1) 

3

 -12x² + 8x - 20

–4(3x² – 2x + 5) 

4

3x³y + x²y²

x²y(3x + y) 

5

6x² + 36x + 48

6(x + 4)(x + 2) 

D

1

x² - 25

(x-5)(x+5)

2

2x^3-3x^2-9x

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

3

15x^2y^4-10x^3y^2

5x^2y^2(3y^2-2x)

4

4x^2-25x-21

(4x+3)(x-7)

5

-32x^2+2

-2(4x+1)(4x-1)

E

1

Is this factored completely:

 3x²(x² + 9). Why or why not?

Yes, there are no more common factors between x² and 9 and an adding sign so no difference of squares

2

3x² - 6x - 9

3(x -3)(x + 2)

3

2p⁵ + 10p⁴ - 12p³

2p³(p - 1)(p + 6)

4

9x⁶ + 30x⁵ + 24x⁴

3x⁴(3x+4)(x+2)

5

x² − 16x + 48

(x-12)(x-4)