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# Factoring Polynomial

### Types of Factoring

Step 1 in Factoring . . . Always Look for Greatest Common Factor
Step 2 in Factoring Look at Number of Terms
Three types of Factorable Binomials Difference of Two Squares \\ Sum of Two Cubes \\ Difference of Two Cubes
Three types of Factorable Trinomials Perfect Square Trinomial // "Easy kind" (Leading Coefficient = 1) // "Harder kind" (Leading Cofficient Not = 1)
How do you attempt to factor polynomials with four terms? By Grouping
Identify: x^2 - y^2 Difference of Two Squares:(x+y)(x-y)
Identify: x^2 + y^2 Sum of Two Squares ~ PRIME!!
Identify: x^3 + y^3 Sum of Two Cubes: Binomial X Trinomial // (x + y)(x^2 - xy + y^2)
Identify: x^3 - y^3 Difference of Two Cubes: Binomial X Trinomial(x - y)(x^2 + xy +y^2)
Identify: x^2 + 2xy + y^2 Perfect Square Trinomial: (x + y) ^ 2
Identify: x^2 + bx + c "Easy Kind": Look for factors of c that have a sum/difference of b.
Identify: ax^2 + bx + c "Harder Kind": Look for factors of a x c that have a sum/difference of b. Rewrite middle term and factor by grouping.
Step 3 in Factoring Make sure you have factored completely.
Step 4 in Factoring . . . Always Check your answer!!!
Factor: x^2 - 49 Diffence of Two Squares:(x + 7)(x - 7)
Factor: x^2 - 6x + 9 Perfect Square Trinomial:(x - 3)^2
Factor: x^3 - 27 Difference of Two Cubes:(x - 3)(x^2 + 3x + 9)
Factor: x^2 + 25 Sum of Two Squares:PRIME!!!
Factor: 9x^2 - 64 Difference of Two Squares:(3x + 4)(3x - 4)
Factor: 9x^2 - 48x + 64 Perfect Square Trinomial:(3x - 8)^2
Factors of 24 that have a sum of 10 4 and 6
Factors of 24 that have a difference of 10 12 and 2
Factors of 6 that have a sum of 5 2 and 3
Factors of 6 that have a difference of 5 6 and 1
Factors of 12 that have a sum of 7 3 and 4
Factors of 36 that have a difference of 9 3 and 12
Factors of 36 that have a sum of 15 3 and 12
Factors of 36 that have a difference of 16 2 and 18
Factors of 36 that have a sum of 20 2 and 18
Factors of 36 that have a difference of 5 4 and 9
Factors of 36 that have a sum of 13 4 and 9
First step in factoring 4x^2 - 16 Factor out a 4
Factor: 25x^2 + 81 Sum of Two Squares: PRIME!!
Created by: milesdl