Two Step Factoring with a GCF:



Two Step Factoring with a GCF:

Whenever you are factoring, whether it’s a trinomial, D.O.T.S. problem, or a Case II Trinomial, the 1st step is always the same. Look for the GCF (greatest common factor). If there is no common factor, you proceed to factor using your factoring rules. If there is a GCF, factor with the GCF 1st and then proceed to factor using you factoring rules.

Examples:

6x2 – 6x – 72 8x7 + 88x6 + 240x5 3x2 – 108

Step 1: Take out the GCF

Take the greatest common factor (GCF) for the numerical coefficient. When choosing the GCF for the variables, if all the terms have a common variable, take the one with the lowest exponent

6(x2 – x – 12) 8x5(x2 + 11x + 30) 3(x2 – 36)

Step 2: Factor what’s left (if possible) using your factoring rules:

6(x+3)(x-4) 8x(x+6)(x+5) 3(x+6)(x-6)

Practice Problems:

1) 3x2 – 108 2) 6x2 – 6x – 432 3) 5x2 + 55x + 140

4) x8 + 3x7 – 70x6 5) 10x4 – 70x3 + 60x2 6) 16x2 – 144

7) 20x2 – 245 8) 64x9 – 100x3 9) 121x8 - 81

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