00:01
First of all, if negative 8i is a 0, so is positive 8 .i.
00:05
And what that means then is x plus 8i and x minus 8i are factors.
00:14
So what i would do is start to distribute all this out.
00:18
So x times x is x squared.
00:20
You'll have negative 8xi, positive 8xi, and 8i times negative 8i would be negative 64i squared.
00:30
Well, these is will cancel and this i squared equals negative 1.
00:35
So what you're really looking at is x squared plus 64.
00:40
And the reason why i do this work is because if this and this are factors, its product is also a factor.
00:48
Well, now i can use long division, which actually isn't that long, and show that it's a factor of x to the fourth plus 55x squared minus, 576.
01:09
I don't really like how lazily i wrote this division, so let me kind of clean that up.
01:15
And so what's my work? x squared times x squared will give me x to the fourth, but then i have to multiply x squared by that 64...