Factoring strategy

Learn how to choose the best factoring strategy when factoring polynomials. The following is just a guideline so you know how to approach the problem without wasting too much time using the wrong approach.

Step 1.

Are there any common factors? If so factor out the greatest common factor (GCF)

Step 2.

How many terms does the polynomial have?

1. If there are two terms, decide if one of the following can be used to factor the polynomial.

a. Difference of two squares: a2 - b2 = (a - b)(a + b)

b. Sum of two cubes: a3 + b3 = (a + b)(a2 - ab + b2)

c. Sum of two squares: a2 + b2   cannot be factored!

d. Difference of two cubes: a3 - b3 = (a - b)(a2 + ab + b2)


2. If there are three terms, try one of the following.

a. Perfect square trinomials: a2 + 2ab + b2 = (a + b)2 or a2 - 2ab + b2 = (a - b)2

b. If the polynomial is not a perfect square trinomial, then factor using the method used to factor trinomials of the form ax2 + bx + c.

If a = 1, look for factors of c that will add up to b.

If a is not equal to 1, factor the first term, factor the last term, and try all the different combinations until you get the correct one.

3. If there are 4 or more terms, try factoring by grouping.

Step 3. Check to see if the factored polynomial can be factored further.

Step 4. Check my multiplying.

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