ShmoopTube

00:04

Factoring Polynomials by Grouping, a la Shmoop.

00:08

Grunkle, Goblinville's newest Architect, is having trouble constructing a hovel.

00:13

His hovel... looks like this:

00:15

If he doesn't finish it by sundown, he will look like this:

00:20

Can you help Grunkle simplify his blueprints?

00:23

The area of the hovel floor should be x2 + 3x + 2x + 6.

00:28

All those polynomials are making Grunkle rather blue.

00:32

Which is unfortunate, since Grunkle is usually a lovely emerald green.

00:35

Good thing we can factor this polynomial by grouping.

00:39

The first two terms have a common factor of x

00:42

and the last two terms have a common factor of 2.

00:45

We can rewrite the polynomial as x times x + 3 + 2 times x + 3.

00:55

See another factor we can pull out?

00:57

Since both terms have x plus 3 as a factor, we can pull out an x plus 3 from each.

01:04

This gives us (x + 2) times (x + 3).

01:08

Happy factorization, Grunkle!

01:10

All you have to do now is look at your blueprint to see what x is.

01:14

And x equals... the length of a ferocious jungle jabberwocky.

01:18

Sorry, you're on your own.

Full Transcript