00:01
So in this problem, we're being asked to find a polynomial function in factored form that satisfies all the following conditions.
00:07
So i'm actually going to start with the conditions at the bottom.
00:09
So we're told that we have one zero with an even multiplicity and one with an odd multiplicity.
00:14
So let's say that we had a zero, let's say x was equal to three, and this had an even multiplicity.
00:19
Let's say the multiplicity was two.
00:21
Then we have an odd multiplicity, or another zero, let's call it negative one, and it has an odd multiplicity.
00:27
Let's call it 3.
00:29
So if we were the right disin factored form, remember to get from your zeros to your factors, use the opposite sign.
00:34
So if 3 is a 0, we know that x minus 3 is a factor.
00:38
And if negative 1 is a 0, we know x plus 1 is a factor.
00:41
Now, the multiplicity tells us what the exponent for our factor will be.
00:45
So for x minus 3, the exponent will be 2.
00:48
And x plus 1, it'll be 3.
00:50
Now, we're also told we have two imaginary zeros.
00:53
So let's say one of our imaginary zeros was i.
00:55
Well, that would mean that its complex conjugate also has to be a zero.
00:59
So that would be negative i...