Question

use synthetic division to find P(-3) for P(x)=x4-2x^3-4x-4 step by step please...

Answer 1

Have you ever done Synthetic Division?

Answer 2

no ...I need a lot of help

Answer 3

One background question, first. Why have you been given a Synthetic Division Problem without also having been given the tools to accomplish the task? Are you in an on-line class that hasn't a clue? What's the deal?

Answer 4

i have a on-line class, which i hate

Answer 5

Fair enough. Let's see of we can get through this one without much trouble. You'll be okay.

Synthetic Division is super awesome. It does two important things - AT THE SAME TIME!!! It turns a very complicated expression into a few arithmetic operations and it evaluates polynomials (like yours) rather quickly.

Typically, we just build a little arrangement of numbers and wade through it. There is one important thing to remember before ploughing through. Synthetic Division likes only COMPLETE polynomials. If there is a piece missing, you have to go get it.

In your case, \(P(x) = x^{4}-2x^{3}-4x-4\) has a little problem. The \(x^{2}\) term is missing. GAAAaaa!!!

Kidding. It's not all that big a deal. You just have to include one. It looks a little funny, at first.

\(P(x) = x^{4}-2x^{3} + 0x^{2}-4x-4\)

See what happened? I added the \(x^{2}\) term, but made the coefficient zero (0) so I would not be changing the nature of \(P(x)\).

Whew!! Let's stop there for a second and see if I managed to make ANY sense at all.

Answer 6

why did you add the other x

Answer 7

Do you mean the \(x^{2}\)? You must read very carefully. Every word might be a clue.

Synthetic Division likes only COMPLETE polynomials. If there is a piece missing, you have to go get it. In your case, \(P(x)=x^{4}−2x^{3}−4x−4\) has a little problem. The \(x^{2}\) term is missing.

You must add the \(x^{2}\) term (are any other term in the sequence that happens to be missing).

Answer 8

oh i get it now, and i don't think nothing is missing now

Answer 9

You have to get them all. Line up all the terms in descending order and see which are missing. Fill in any that are absent. After that, we are going to ignore all the 'x's and just use the coefficients.

Answer 10

It usually looks something like this:

Answer 11

oh..ok

Answer 12

Have you seen something like that?