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# Factoring: A General Strategy

Recall:

The factoring methods that you should have in mind:

1. Factoring out the gcf.
2. Factoring by grouping (4 term polynomials only).
3. Shortcut for factoring x 2 + bx + c.
4. Guess-and-check method for factoring ax 2 + bx + c .
5. ac -method for factoring ax 2 + bx + c .
6. Formulas for factoring perfect-square trinomials.
7. Formula for factoring a difference of squares.

New Stuff:

Procedure: (Factoring a Polynomial)

1. Always start by factoring out the gcf.

2. Look at the number of terms. What you do next depends on this number.

a) If there are two terms, check to see if it is a difference of squares. If it is, use the formula. If it is a sum of squares, then you cannot factor it any more.

b) If there are three terms, factor it using methods 3, 4 or 5 (depending on a ) or, if it’s a perfect-square trinomial, you could try using a formula from the methods 6 or 7.

c) If there are four terms, try factoring by grouping.

3. Check each one of the factors that you have. If any can be factored further, do it.

4. (Optional, unless instructed to do so) Check by multiplying.