MTH 091 Section 11.3/Section 11.4 Factoring Trinomials By Grouping Factoring Trinomials Using FOIL

Something Different In the previous section, we were factoring trinomials of the form x 2 + bx + c. Generally speaking, we were looking for two numbers that added to make b and multiply to make c. That strategy will not work if the first term has a coefficient—in other words, we are looking at trinomials of the form ax 2 + bx + c.

Two New Strategies Using Grouping (The AC Method) Using FOIL (Educated Guess and Check)

The AC Method 1.Make sure your trinomial is in the form 2.Multiply the first and last terms together.

Continued 3.List all the factors of the product you found in Step 2. In this case you must consider the sign. 4.Find the pair of factors that add up to equal the middle term of your trinomial. 5.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.

Educated Guess and Check 1.Determine the signs of your factors based on the signs of your trinomial: If the last sign is positive, then use two of the first sign. If the last sign is negative, use one positive and one negative.

Continued 1.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 3.Choose a pair of factors from each list and plug them into your parentheses. FOIL to determine which combination gives the desired middle term. a.No choice is the best choice b.Pick towards the middle c.Never make a factor that has a factor. d.Evens can’t make odds and odds can’t make evens.

Examples 21x 2 – 41x x x – 63 25n 2 – 5n – 6 2x 2 + 7x – 72 2a ab + 5b 2 42a 2 – 43a x 2 – 49x + 15

Two Important Statements 1.Use the FOIL Method to check your factoring. 2.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 12x 2 – 14x – 10 8x 2 y + 34xy – 84y 5x 2 – 75x x 2 + 4x x x – 14 6x 3 – 28x x 42x 4 – 99x 3 y – 15x 2 y 2