Section 6.2 Factoring Trinomials

Overview This factoring strategy is generally applied to polynomials with three terms. Remember, however, to first look for a GCF.

The Big Idea Recall that the FOIL method is often used to find the product of two binomials:

Two Strategies Educated Guess and Check (Trial and Error) The AC Method (Grouping)

Educated Guess and Check Determine the signs of your factors based on the signs of your trinomial term + term + term = ( + )( + ) term – term + term = ( - )( - ) term + term – term = ( + )( - ) term – term – term = ( + )( - )

Continued Factors of F and Factors of L: List all the possible factors of the first term and the factors of the last term. Do not be concerned about the sign of the last term.

Continued Choose a pair of factors from each list and plug them into your parentheses. FOIL to determine which combination gives the desired middle term. No choice is the best choice Pick towards the middle No factor with a factor Evens can’t make odds

The AC Method Make sure your trinomial is in the form 2. Multiply the first and last terms together.

Continued List all the factors of the product you found in Step 2. In this case you must consider the sign. Find the pair of factors that add up to equal the middle term of your trinomial. Replace the middle term with the fair of factors. You now have a polynomial with four terms instead of three. Use factor by grouping to complete your factoring.

Examples z2 + 2z – 24 z2 + 8zw + 15w2 2x2 + 13x + 15 20r2 – 27r – 8 -15y2 + 17y + 18 14c2 – 17cd – 6d2 2m2 + 17m + 10

Two Important Statements Use the FOIL Method to check your factoring. Whether you choose to use the “Educated Guess and Check” method, the “AC” Method, or some other method, be sure to first check for a Greatest Common Factor.

More Examples -9k3 – 36k2 + 189k 4p4 + 24p3 – 64p2 12x2 – 14x – 10 8x2y + 34xy – 84y 3x2 – 42x + 63 10x4 + 25x3y – 15x2y2