Question

Factor by grouping (sometimes called the ac-method). 11x2+20x-4

First, choose a form with appropriate signs.
Then, fill in the blanks with numbers to be used for grouping.
Finally, show the factorization.

Answer 1

(11x - 2) * (x + 2)

Explanation:

Factoring by grouping is a method of factoring when the leading coefficient is not 1.

Steps for Factoring

Firstly, we should go over the steps in factoring by grouping. Remember that quadratic functions are written in the form ax² + bx + c. The first thing we need to do is find 2 numbers whose product is equal to a*c and whose sum is equal to b. Then, use these numbers to replace b. Next, factor out the GCF of the first 2 terms and the last 2. Finally, group the remaining terms together.

Factoring by Grouping

Now that we know the steps, we can actually factor the quadratic we were given. Firstly, rewrite the equation.

• 11x² + 20x - 4

Then, find the 2 numbers we can use to replace b. The product of 11 and -4 is -44. The two factors whose product is 20 and whose sum is -44 are 22 and -2.

• (11x² + 22x) + (-2x - 4)

Next, factor out the greatest common factor from each binomial.

• 11x(x + 2) - 2(x + 2)

Finally, combine the remaining terms.

• (11x - 2) * (x + 2)