00:03
Okay, here number 44.
00:06
Again, we want to simplify this rational expression, and it's going to require some factoring, of course.
00:13
You may recognize the denominator, right, q squared minus four.
00:17
That's just a difference of two squares.
00:19
Factors q plus two, q minus two, okay? but i'm not going to write in factored form yet because if you know how to handle the numerator, okay, we have four terms in the numerator, which means you're going to have to have to factored by grouping, two terms by two terms.
00:38
So those two terms go together, those two terms go together.
00:43
Now, if you notice, there is a q squared kind of sort of and a minus four kind of sort of there, right? you see it? i mean, if you divide out a q from both of those, you get q squared minus four.
01:01
So that leads me to believe that maybe q squared minus four might be in the numerator too.
01:08
Now, it's no big deal.
01:09
It's just one extra step to factor it out.
01:11
But i'm going to leave the q squared minus 4 in the denominator for just a moment until i see what comes out of the numerator.
01:17
Then if we need to factor the denominator, we will.
01:20
All right.
01:21
So how do we factor these two by two? well, just factor out the gcf.
01:28
Out of q to the third plus three q squared, i can factor out of q squared...