00:01
I'm not sure exactly how your teacher has approached this problem, but when you're looking at x -cube minus 11x squared, i'm not seeing the x squared, but it makes sense of all the things plus 43x minus 65, that if you're looking for the roots or the factors, well, the roots you would set equal to zero, and then the possible roots need to be factors of this number.
00:30
So you're looking at 1, 5, 13, 65.
00:36
And you could guess and check.
00:37
Now, i actually use a calculator, and i saw that.
00:41
And these could all be positive or negative, but the one that works is 5.
00:44
I'm using synthetic division to show this because i'll get a remainder of zero.
00:52
So bring the one down and multiply by what's in the box, adding straight down and multiply, adding straight down and multiply and then add straight down and that's exactly what was supposed to happen.
01:05
So x equals 5 is a root.
01:09
So that means its factor would be x minus 5 and then we're left with x squared minus 6x plus 13 from the synthetic division...