Question

Create your own third degree polynomial that when divided by x + 2 has a remainder of –4. Can someone please help me...

Answer 1

If take something that is `3rd degree` and divide it by something that is `1st degree` then the result we get should be something to the `2nd degree`.

Remember how exponents work?
When you divide terms of similar bases, you `subtract` the exponents.

Example:\[\large \frac{x^3+stuff}{x+2} \qquad=\qquad x^2+stuff+\frac{remainder}{x+2}\]

The x^3 divided by the (x+2) gives us a leading term of x^2 as a result.

Answer 2

Oh I should be careful the way I write that, the stuff in the answer maybe i should have called "other stuff".. It's not the same stuff as in the first part :x

Answer 3

But anyway, they're telling us to come up with our on 3rd degree .. so we have a lot of freedom.

Let's just let the "leftover stuff" be zero.

So we start with this,\[\large x^2+\frac{remainder}{x+2}\]They told us our polynomial, when divided by x+2 will have a remainder of -4.

\[\large x^2+\frac{-4}{x+2}\]

Answer 4

To get our 3rd degree polynomial we just have to undo the division that happened.

Combine the fractions and then your polynomial that you're looking for is your numerator.

Answer 5

So basically, I could use something like this to answer it.. y=x^3+2x^2-4 . It kinda seems like it would work and it has the -4..... I am not really good at this stuff so I don't really know if it is correct

Answer 6

So you combined the fractions and that's what you ended up with?
Yah, good job! :)

They wanted you to come up with your own polynomial, so there won't be only one solution that you could come up with.

We chose to let the "leftover stuff" equal zero so it gave a nice easy answer.

Answer 7

Okay thank you so much! :)