00:01
In this problem, we need to find a polynomial given that the zeros are 4, 4, and 5, and the degree is 3.
00:11
Right, so the first thing we're going to do is change each of the zeros into a factor.
00:17
And the factor will have the opposite sign.
00:21
So if the 0 is 4, the factor will be x minus 4.
00:27
All right, then we have x minus four again.
00:32
And then the five will be x minus five.
00:38
All right, so the first thing i'm going to do is foil the x squared minus four.
00:46
And that will give me first is x squared, outer minus 4x, inner minus 4x, and last will be plus 16.
00:59
All right, we'll do a little bit of cleaning up, gather the last.
01:03
Terms negative 4x plus negative 4x will give me negative 8x plus 16 right then we still have to multiply by the x minus 5 right just for organization i like using a box to multiply anything larger than a 2 by 2 so i'll take the x squared minus 8x and 16 and x minus 5.
01:43
All right, so i'll take the x and multiply it by everything on the top.
01:47
So x times x squared is going to give me x to the third.
01:53
X times negative 8x will give us negative 8x squared...