Choosing a Strategy for Factoring a Polynomial

1. Choosing a StrategyforFactoring a Polynomial

2. 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.

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.

4. 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.

5. Trinomial • If it is a complete square trinomial, use the formula. • If it is a trinomial in the formor or, then use the appropriate factoring method. 2.

6. 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.

7. 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.

8. 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.

9. Practice Problems 1. 2. 3. 4. 5. 6. 7. 8.

10. Answer Key to Practice Problems 1. 2. 3. 4.) 5. 6. 7. 8.