Factoring Polynomials

Factoring

100

y³+9y²

y²(y+9) 

200

3x²y+6xy

3xy(x+2)

300

x²+9x+20

(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

192x² y + 72x³ − 24rxy − 9rx²

3x(8x − r)(8y + 3x)

500

105xuv + 60xv − 70xu − 90xv²

5x(7u − 6v)(3v − 2)

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 difference or sum of perfect cubes

• Factoring second degree polynomials

• Common monomial factor

• Completing the square

400

15x²-18x-24

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

500

what is the inverse process of factoring polynomials

multiplying polynomials

Completing the Square

100

What should be added to complete the square:

x²+10x

25

200

What should be added to complete the square:

f²-6f

9

300

What should be added to complete the square:

d²+9d

(9/2)²

400

What should be added to complete the square:

t²+8t+12

4

500

What should be added to complete the square:

x²-3x-0.25

2.5

Squares or Cubes

100

x²-9

(x+3)(x-3)

200

x³-27

(x-3)(x²+3x+9)

300

4x²-9y²

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

400

8x³+64y³

(2x+4y)(4x²-8xy+16y²)

500

16p⁴-81

(4p²+9)(2p+3)(2p-3)