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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

Factors of +8: 1 & 8

2 & 4

-1 & -8

-2 & -4

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Factoring Polynomials

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Lets do another example:

Lets do another example:

Find a GCF

Factor trinomial

Donít 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!

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

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Factoring Polynomials

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

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

O + I = 30 x - x = 29x

This doesnít work!!

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

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

This doesnít work!!

Switch the order of the second terms

and try again.

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Try another combination:

Try another combination:

Switch to 3x and 2x

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Factoring Technique #3

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!

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?

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?

Does the middle term fit the pattern, 2ab?

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

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Factoring Technique #4

Factoring Technique #4

Factoring By Grouping

for polynomials

with 4 or more terms

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Factoring By Grouping

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).

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