00:02
Given the function f of x equals x to the third plus 2x squared minus 5x minus 4 and k equals negative square root of 5, we're going to rewrite this in the form of f of x equals x minus k times q of x plus r of x.
00:18
We actually already know x minus k because we're given our k value, so that's going to be x minus the negative square root of five.
00:25
So it's going to turn into x plus the square root of five.
00:28
Q of x is our next part of the factor.
00:30
We're going to use synthetic division to determine what that is.
00:34
And r of x is our remainder.
00:37
It's going to be whatever is left over that we can't fit into that factor.
00:41
So we're going to use synthetic division.
00:44
Here inside this, i just write the coefficients.
00:48
I'm not going to write the terms.
00:49
So it's 1x cubed plus 2x squared minus 5x minus 4.
00:58
So we just write the numbers...