Factoring Polynomials

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3. The product of last terms of both binomials must equal last term of the trinomial (c).

4. Think of the FOIL method of multiplying binomials, the sum of the outer and the inner products must equal the middle term (bx).

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Factors of +8: 1 & 8

2 & 4

-1 & -8

-2 & -4

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Lets do another example:

Find a GCF

Factor trinomial

Don’t Forget Method #1.

Always check for GCF before you do anything else.

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When a>1 and c<1, there may be more combinations to try!

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Step 3: Place the factors inside the parenthesis until O + I = bx.

O + I = 30 x - x = 29x

This doesn’t work!!

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O + I = -6x + 5x = -x

This doesn’t work!!

Switch the order of the second terms

and try again.

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Try another combination:

Switch to 3x and 2x

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Factoring Technique #3

continued

Factoring a perfect square trinomial in the form:

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Perfect Square Trinomials can be factored just like other trinomials (guess and check), but if you recognize the perfect squares pattern, follow the formula!

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Does the middle term fit the pattern, 2ab?

Yes, the factors are (a + b)2 :

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Does the middle term fit the pattern, 2ab?

Yes, the factors are (a - b)2 :

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Factoring Technique #4

Factoring By Grouping

for polynomials

with 4 or more terms

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Factoring By Grouping

1. Group the first set of terms and last set of terms with parentheses.

2. Factor out the GCF from each group so that both sets of parentheses contain the same factors.

3. Factor out the GCF again (the GCF is the factor from step 2).