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Factoring Polynomial
Types of Factoring
| Question | Answer |
|---|---|
| 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
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