00:01
All right, so we want to solve this to third degree polynomial equation.
00:06
All these factors are divisible by three.
00:08
So let's go ahead and factor and see what happens.
00:10
We can factor by grouping.
00:11
Let's factor out an x squared here.
00:14
Then we're left with x minus 21.
00:18
And then we have plus.
00:21
So let's see.
00:24
343 divided by 147 doesn't work.
00:27
Okay, let's see.
00:29
What's 147 divided by 21 is 7? 343 divided by 21.
00:35
That doesn't work.
00:37
Okay, they're both divisible by 49.
00:39
So let's pull out 49.
00:42
And then we'll get 3x minus 343 divided by 49 is 7.
01:02
So that doesn't work to factor by grouping.
01:06
But we have a bunch of things that look like there are multiples of 7 here.
01:10
So let's see, is 7 a root of this equation? 7 cubed minus 21 times 7 squared, which is 49, plus 147 times 7 minus 343, does that equal 0? 7 cubed is 343 minus 343, so that cancels out, and then 21 times 49 is the same thing as 147 times 7.
01:40
Yep.
01:41
So this is true...