Factoring a polynomial means expressing it as a product of other polynomials.
Choosing a Strategy for Factoring a Polynomial. You have learned various strategies for factoring...
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Transcript of Choosing a Strategy for Factoring a Polynomial. You have learned various strategies for factoring...
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.
.
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 .
1.
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.
1.
2.
3.
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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