00:01
Given this function, f and two factors 2x minus 1 and x plus root 5, we have a series of questions to answer.
00:09
The first being verify that the given factors are indeed factors.
00:15
So we can either use synthetic or long division to get remainders of zero.
00:19
This is one way to verify this.
00:22
Our factor x plus root 5 is in of a style that would allow us to say, all right, let's synthetically divide the negative square root of five from our coefficients 2, negative 1, negative 10, and 5.
00:36
If we get a remainder of a 0, this verifies it is the solution.
00:38
Let's check it out.
00:39
Drop down the 2, multiply, add, multiply.
00:50
And this would be come, let's see, 10 plus root 5.
01:05
And then when we add, the tens will cancel, we just have, root 5 and then when we multiply these together we'll get negative 5 and then a remainder of 0 so that checks there now the next one 2x minus 1 we don't want to do that one we're probably going to want to do long division we're going to do this with the what we have left over would be 2x squared plus negative 1 minus 2 root 5 x plus root 5x plus root let's see how this goes.
01:58
Well, we start with the first one.
02:00
2x squared divided by 2x is just x.
02:05
Distribute, we get 2x squared minus x...