Factoring Polynomials

Factoring

100

3y⁴+27y²

3y²(y² + 9) 

200

3x³y + 6xy + 3xy³

3xy(x + 1)²

300

5x² - 45x + 100

5(x - 5)(x - 4)

400

2y² - 16y + 32

2(y - 4)²

500

4x³ - 25x² + 6x

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

Grouping

100

m³ − m² + 2m − 2

(m² + 2)(m − 1)

200

12a³ − 9a² + 4a − 3

(3a² + 1)(4a − 3)

300

ay - yx - x² + ax

(y+x)(a-x)

400

Completely factor:

2x⁴  + 4x³ − 16x − 32

2(x + 2)(x - 2)(x² + 2x + 4)

500

Completely Factor:

x⁶ - 4x⁴ + 9x² - 36

(x + 2)(x - 2)(x⁴ + 9)

Trivia!

100

what does is mean when a polynomial is prime?

A polynomial with integer coefficients that cannot be factored into polynomials of lower degree

200

What does it mean to factor a polynomial?

Factoring polynomials involves breaking up a polynomial into simpler terms so when  the terms are multiplied together they equal the original polynomial.  

300

Name 4 factoring strategies

• Grouping 

• Finding the difference of perfect squares

• Finding the sum or difference of perfect cubes

• Box

• Greatest Common Factor (GCF)

• X Method

• Quad-like (higher degree)

• Completing the square

400

Completely Factor

15x²-18x-24

3(5x+4)(x-2)

500

Completely Factor

9x(11x + 13) - 55(11x + 13)

(9x - 55)(11x + 13)

Quad-Like

100

Completely Factor

x⁴ + 50x² + 625

(x² + 25)²

200

Completely Factor

x⁴  - 20x² + 64

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

300

Completely Factor

x⁶  - 2x³ + 48

(x³ + 6)(x + 2)(x²  - 2x + 4)

400

Completely Factor

4x⁴  + 140x² - 144

4(x² + 36)(x + 1)(x - 1)

500

Completely Factor

9x⁴  + 77x² - 36

(x² + 9)(3x - 2)(3x + 2)

Squares or Cubes

100

400x² - 36

4(10x+3)(10x-3)

200

16x³ - 54

2(2x - 3)(4x² + 6x + 9)

300

4x⁴ - 9y⁴

(2x² + 3y²)(2x² - 3y²)

400

64x⁶+512y³

64(x² +2y)(x⁴ - 2x²y + 4y²)

500

Completely Factor

80p⁴ - 405

5(4p² + 9)(2p + 3)(2p - 3)