00:01
This problem asks us to factor this trinomial 4x cubed plus 8x squared plus 12x.
00:09
I'm going to use a strategy that i've used in the past called double division.
00:13
In this case, it's triple division because there are three terms.
00:17
Common factors go on the outside of an upside down long division setup.
00:25
And so that means that the answers will go below instead of above.
00:28
When i'm finished, my problem will look like the greatest common factor on the outside and the three remaining terms from which that greatest common factor was divided away.
00:42
So i'll begin by looking at these three numbers and thinking about numbers that make them.
00:47
I know that two times two and one times four gets me four.
00:52
One times eight and two times four gives me eight.
00:56
1 times 12, 2 times 6, and 3 times 4 give me 12.
01:03
Factors that they shared were 2 or 4.
01:06
And so since 4 is something they all share, i'm going to put a 4 on the outside.
01:11
I'm going to divide each term by 4.
01:14
So 4 goes into 4 1 time, 4 goes into 8, 2 times, and 4 goes into 12, 3 times.
01:22
The next thing i'm going to do is look at the variables.
01:25
I notice that there's x to the third power, which is x times x times x, x to the power of 2, which is x times x, and then x, or x to the power of 1.
01:38
Now, i need to take the smallest number of things that they share, because if i take anything bigger, it won't be able to be taken or divided from all of the terms.
01:49
This has to be common or shared factors.
01:52
So they each have one of the xes.
01:55
If i remove one of the xes from the last term, there is no longer any variable...