Question

MEDAL AND FAN. Use synthetic division and the given factor to completely factor the following polynomial: x^3-x^2-24x-36; (x-6)

If you could explain it to me, I'll do the math for each step.

Answer 1

Do you know how to do synthetic division?

Answer 2

Nope.

Answer 3

Awesome.

Answer 4

Heh.. I'm a fast learner? Try me.

Answer 5

So what you need to do with synthetic division is take all the coefficients of the polynomial and list them from them from left to right.

Answer 6

Okay, coefficients, left to right. Can we maybe work through an example problem..? I don't want you to feel like you're handing out answers.

Answer 7

Also, though it does not apply to this problem, you need to make sure to include 0 when a power is missing. For example. x^3+4x+4. List the coefficients, it would be 1, 0, 4, 4

Answer 8

Because normally there is an x^2

Answer 9

Okay. I'm following so far. But there is an x^2?

Answer 10

So here it would be 1,-1,-24,-36

Answer 11

Yes.

Answer 12

Okay. HAven't lost me yet.

Answer 13

For the x^2 thing. The form of a polynomial is ax^n+bx^n-1+cx^n-2...z. Thus you need to account for the coefficients of the all the powers

Answer 14

coefficients of powers 1-3? or just from 1- the highest power listed, filling in for the missing?

Answer 15

Okay I think I am making my explanation more complicated than it needs to be. Let's focus on solving the problem at hand.

Answer 16

Sounds good lol.

Answer 17

You are given that (x-6) is a factor of the polynomial. Thus when x=6, the expression will equal 0.

Answer 18

@ArkGoLucky try using the drawing tool t show how synthetic division works :P