00:01
For this question, we are going to write a polynomial function that satisfies the given conditions.
00:06
The given conditions include that we want lowest degree, lowest possible integer coefficients, and we have zeros that have been given.
00:17
We have been told that x equals zero with a multiplicity of three, and that x is 8 minus 5i.
00:29
Whoops, i did not write that correctly.
00:31
8 is equal to 8 minus 5i.
00:36
If that 0 is included, we must also include its conjugate.
00:43
If i write these as factors, the factors will be x times x times x times x minus 8 plus 5i because i distributed the subtraction and x minus 8 minus 5i.
01:06
Let's multiply.
01:09
We have x cubed times x squared.
01:20
I'm distributing the x.
01:22
X squared minus.
01:27
You know what? i'm going to show you something different.
01:28
Let me back up.
01:30
Sometimes when i'm multiplying by such big polynomials, i'm multiplying big polynomials together.
01:37
I'll do a times table to help organize my work.
01:43
This is a good opportunity to show you...