GCF and Factoring Trinomials - GCF and Factoring Trinomials...

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GCF and Factoring Trinomials Factoring Out the Greatest Common Factor (GCF) Consider the example x (x - 3) = x 2 - 3x We can do the process in reverse: Look at x 2 - 3x and notice that both have a common factor of x . We can pull out the x terms (use the distributive property in reverse). x 2 - 3x = x (x - 3). Example: Consider the expression 2x 3 - 4x 2 A. Find the GCF B. Pull it out. Solution: A. The GCF is 2x 2 B. We can write 2x 3 - 4x 2 = 2x 2 (x - 2) Exercises: A. Find the GCF B. Pull it out. 1. x 2 - 5x
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2. 5xy + 25y 3. 3x(2 - x) + 4(2 - x) 4. 6x 2 y 3 - 8x 2 y 2 + 10x 4 y 4 Factoring by Grouping Consider the expression 3x 2 + 6x - 4x - 8 We can factor this by grouping two at a time: (3x 2 + 6x) - (4x + 8) We now pull out the GCF of each: 3x (x + 2) - 4 (x + 2) Pull out the GCF again: (3x - 4) (x + 2) Exercises Factor the following by grouping: A. 3x 2 - 6x + x - 2 B. x 3 - 3x 2 + x - 3 Factoring Trinomials With constant Leading Coefficient Consider the trinomial: x 2 + 5x + 4
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We want to factor this trinomial, that is do FOIL in reverse. Since the leading coefficient is 1 we can write: x 2 + 5x + 4 = (x + a) (x + b)
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