00:01
So in this question, we want to find the complex zeros of the polynomial function and write our function f in factor four.
00:09
So my function is f of x equals xq minus 8x squared plus 25x minus 26.
00:16
Before i find my complex zeros, i'm going to find my real zeros.
00:22
So i'm going to head to my calculator.
00:24
And what i've done here is i've graphed our function x cubed minus 8x squared plus 25x.
00:32
Minus 26.
00:35
And when i graph this, it looks like there's a zero around x equals two.
00:41
So let's see if x equals two is actually a zero or not.
00:46
To do this, i'll use synthetic division.
00:50
So i'm going to line up my coefficients on f, 1, negative 8, 25, and negative 26.
01:00
And i'm going to use 2 as my multiplier.
01:06
With synthetic division, i drop down the 1.
01:09
Multiply by 2.
01:12
Add, multiply by 2, add, multiply by 2, add, multiply by 2, and sure enough i get 0, i get a remainder of 0.
01:25
And so that means that 2 was a 0, and that therefore x minus 2 was a factor.
01:35
My other factor is quadratic, and the coefficients are given in that synthetic division...