Choosing a Strategyfor

Factoring a Polynomial

You have learned various strategies for factoring different polynomials but when given a random polynomial with a general instruction to factor it, where do you start?

This presentation shows how to approach factoring any polynomial step-by-step.

Consider the following examples:

1. 2. 3.

STEP 1: Do all terms of the polynomial have a common factor? If yes, factor it out.

1. 2. 3.

There is no common factor, so move on to the next step.

STEP 2: Consider the number of terms of the polynomial.

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Binomial

Can only be factored if it is

• A difference of two squares: use the formula .

• A sum of two cubes: use the formula .

• A difference of two cubes: use the formula .

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Trinomial

• If it is a complete square trinomial, use the formula .

• If it is a trinomial in the form or or , then use the appropriate factoring method.

2.

Four-Term Polynomial

• Factor by grouping.

• If the grouping of the first terms and the last terms does not work, try exchanging the order of terms.

• If there are two cubes, group them together.

3.

STEP 3: Consider if any of the resultant factors can be factored further.

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None of the polynomials in parenthesis can be factored further.

Summary

Step 1: Factor out the greatest common factor, if any.

Step 2: Check the number of terms:• Is it a binomial? Check if it is a difference of two squares or sum of a

difference of two cubes. Otherwise, it is prime.• Is it a trinomial? Check if it is a complete square or use the method for

factoring trinomials in the form or or .• Is it a four-term polynomial? Factor by grouping.

• If grouping first two and last two terms does not work, exchange the order of terms.

• If there are two cubes, group them together.

Step 3: Check if any of the resultant factors can be factored further.

Practice Problems

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Answer Key to Practice Problems1.

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