Factoring by Grouping 04:05 minutes

Video Transcript

Transcript Factoring by Grouping

Adventure Mike and his girlfriend plan to build a treehouse. Using a snake as a measuring stick, Mike figured out the polynomial expression to represent the total area.
Oh jeez, his girlfriend just remembered – she wants a balcony, so she and Mike can watch the sunset. What can he do? She’s the romantic type. So, to save time, rather than measuring and calculating everything all over again, he can use grouping to factor polynomials.

Standard Form of a Quadratic Polynomial

Let’s take a look at the expression he wrote, 15x²+9x-6. Hmm. This looks familiar, doesn’t it? This expression is in the standard form of a quadratic polynomial, ax²+bx+c, but notice it's a trinomial and 'a' is equal to a number other than 1. To figure out the measurements for the sides of the treehouse, how can Mike factor this expression?

Multiplying Binomials

To show him how to factor by grouping, let’s use another problem as an example. To put this method into perspective, we'll start at the end result, with the factors. Working backwards, first, use the FOIL method to multiply the two binomials. Before combining like terms, we have 3x² + 6x – x – 2. To help you understand factoring by grouping, pay attention to the terms that are highlighted. After combining these like terms, the result is a trinomial in standard, quadratic form with 'a' equal to a number other than 1.

Finding the factored form

Let’s work on Mike’s problem. Okay, so how do you get from the standard form to the factored form when 'a' is not equal to 1? There's a little trick to doing this. We need to find the factors of 'ac' that sum to 'b'. a = 15 and c = -6. So since 'ac' = -90, here's a list of some of the factors of -90 – let's take a look. Hmm can you find the pair of factors that also sum to 9? That's right. -6 and 15 are factors of -90 and sum to 9.
Now, watch carefully while I do some mathemagic. Write two new terms using the factors of 'ac' that sum to 'b', and multiplied by 'x'.
Does this format look familiar? Remember the highlighted terms - from the example problem? Now to group, use parentheses to group the four terms into two binomials. This is a little tricky because you have to group the terms so that, when you factor out the GCF, the remaining binomial is the same for each. Also, be especially careful you don't make a sign error. Last step, combine the two GCFs, to create a new binomial. The polynomial is factored!

Adventure Mike has the measurements for the two sides of the treehouse. If his girlfriend wants a bigger treehouse, it won’t be a problem because he can just adjust the size of the sides.

Let’s fast forward, the treehouse is finally finished. To remember the special moment, Adventure Mike snaps some photos. Let's look Oh no! It seems like Mike has been alone in the jungle - just a little too long…