00:01
We're being asked to factor the given polynomial completely.
00:03
To do this, i'm going to use the substitution method.
00:06
So off to the side here, i'm going to let x equal this quantity to y plus 1.
00:13
So now i'm going to substitute x in place of 2y plus 1, and when we do this, we're going to get y to the 4 minus x squared.
00:21
So if you notice, this binomial is now the difference of two squares, and therefore can be factored.
00:27
So it will factor to two binomials.
00:29
The first term of both binomials will be the square root of the first term.
00:33
Well, the square of the y to the fourth is y square.
00:37
And the second term will be the square root of the last term, while the square of x squared is x.
00:42
And then remember, one sign will be plus and one sign will be minus.
00:46
So now what i'm going to do is i'm going to substitute 2y plus 1 back in for x.
00:52
So when we do this, we're going to get y squared plus the quantity of 2y plus 1.
00:59
And then we're also going to have y squared minus the quantity of 2y plus 1.
01:06
And now we would just want to simplify.
01:08
Well, in this first factor, there's a plus sign in front of that preemphasy, which won't change anything.
01:13
So we'll simply be left with, and i'm going to put it up here to the top right, y squared plus 2y plus 1.
01:21
And then our second factor in front of that preemphasy, there's a minus sign, which means both factors need to switch signs...