Question

What is the f(x)/g(x) when f(x) = 6x3 - 19x2 + 16x - 4 and g(x) = x - 2?

Answer 1

@Jhannybean

Answer 2

\[
\frac{f(x)}{g(x)} = \frac{6x^3-19x^2+16x-4}{x-2}
\]

Answer 3

You may want to check if \(x-2\) divides the top.

Answer 4

\[
f(2) = 6(2)^3-19(2)^2+16(2)-4 = 6(8)-19(4)+16(2)-4
\]

Answer 5

So sorry for bothering you wio.

Answer 6

The reason I do this is if \(f(2) = 0\), then that means \(x-2\) can be factored out.

Answer 7

Do you know how to divide polynomials?

Answer 8

Yes, I think so.

Answer 9

Okay, first of all, is \(f(2) = 0\)?

Answer 10

I dont know, sorry.

Answer 11

Well, can you try?

Answer 12

We need to keep simplifying this:\[
f(2) = 6(2)^3-19(2)^2+16(2)-4 = 6(8)-19(4)+16(2)-4
\]

Answer 13

Okay. How is it that all these terms dont have the same x value?

Answer 14

No, they all had \(x=2\), but then I squared/cubed some of them

Answer 15

They need to be multiplied, so I kept parethesis

Answer 16

Oh okay.

Answer 17

So can you do the operations and find out the final value?

Answer 18

Okay, I'll try.

Answer 19

I got: \[f(2)=48-76+32-4=48-76+32-4\]

Answer 20

Okay, now do subtraction and addition to get final result.

Answer 21

\[f(2)=-28+28=-28+28\]

Answer 22

So \(f(2) =0\).

Answer 23

This means you can simplify if you divide out the \(x-2\).
Can you do that?

Answer 24

Okay.

Answer 25

Hmm, what did you get?

Answer 26

^