00:01
So we want to factor this polynomial completely.
00:05
I'm going to rewrite this to make it a little bit easier to see.
00:07
So that's going to be q of x equals x of the 4th minus 625.
00:11
So i'm going to recognize the fact that i can rewrite these in terms of perfect squares.
00:16
For example, x to the 4th is the same as x squared to the second power.
00:22
625 is the same as 25 to the second power.
00:25
So what i want to do is i want to call you my x squared here.
00:28
So that means that if u is equal to x squared, that means u squared is x to the fourth.
00:35
So q of x, i'll rewrite that as u squared minus 25 squared.
00:41
What i have is the difference of two squares.
00:43
So i'm going to factor that into u plus, this is 25 squares.
00:49
So u plus 25 and u minus 25.
00:53
Well, because of that, now u is representing x squared.
00:57
So that means q of x is the same as x squared plus 25 and then x squared minus 25.
01:06
Let's move these over a little bit.
01:14
Get that and that moved over.
01:16
Okay.
01:17
All right.
01:18
So from here, this is also the difference of two squares.
01:22
So i can do q of x as equal to.
01:24
Oh, and actually, if we're going to do this completely, we have to do our complex answers as well.
01:29
So i'll start with the x squared minus 25 that will factor into x plus 5 x minus 5.
01:36
So that's going to be two of my zeros right there.
01:38
I'll have.
01:40
Well, so for my factored form, it actually looks like this, s squared plus 25.
01:46
So that will be the answer here.
01:48
That's going to look like this one.
01:50
Now for the zeros, this will turn into a zero of negative five.
01:54
This will be five.
01:55
So it says here, order your answers from smallest to largest real.
01:58
So small so the x equals negative 5 with a multiplicity of 1...