A polynomial f(x) and one or more of its zeros are...

A polynomial $f(x)$ and one or more of its zeros are given. $f(x) = x^4 - 10x^3 + 71x^2 + 30x - 222$ $5 - 7i$ is a zero Part: 0 / 3 Part 1 of 3 (a) Find all the zeros. Write the answer in exact form. If there is more than one answer, separate them with a comma. Select \"None\" if applicable. The zeros of $f(x)$:

Transcript

00:01 So if negative 3 minus 3i is a 0, then i know negative 3 plus 3i is a 0.

00:08 I'm going to come up with these factors first.

00:17 I'm going to multiply them.

00:21 So that's x plus 3 squared minus 9 i squared.

00:26 X squared plus 6x plus 9 plus 9.

00:30 That's x squared plus 6x plus 6x plus 18.

00:35 Now i'm going to take my f of x polynomial.

00:42 That's 2x to the fifth plus 13x to the fourth plus 29x cubed minus 54x squared minus 198x plus 108.

01:00 I'm going to do some long division.

01:03 So let's do that x squared plus 6x plus 18 into.

01:10 This very long polynomial.

01:26 So x squared into 2x to the fifth is going to go 2x cubed times.

01:31 Let's distribute.

01:40 We're going to draw the line.

01:42 We're going to change the signs.

01:45 So that is going to give me 13 minus 12, 1x to the fourth.

01:51 And i have 29 minus 36.

01:55 So that's going to be minus 7x cubed.

01:58 And i'm going to bring down that.

01:59 54x squared plus x squared and repeat the process i'm going to draw the line and i'm going to change the signs so now i have negative 13x cubed and negative 54 minus 18 that's going to be minus 72x squared minus 198 x keep going so minus 13x that is going to be minus 78 and that will be 18 times 13 is 234 draw the line change the signs cancel so this is going to give me now 78 minus 72 that's 6x squared 234 minus 198...

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