# Create your own third degree polynomial that when divided by x + 2 has a remainder of –4.I'm completely lost on how to do this. I've tried at least 4 times already, and I still can't figure out...

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

I'm completely lost on how to do this. I've tried at least 4 times already, and I still can't figure out what I'm doing. I need a little help, please?

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to remember what reminder theorem states when a polynomial is divided by a linear binomial x-p, then the reminder is a constant equal to f(p).

Hence, since the linear binomial is x+2 and the reminder is -4, then`f(-2) = -4` .

You need to write the third degree polynomial such that:

`f(x) = ax^3 + bx^2 + cx +` `d`

Substituting -2 for x yields:

`f(-2) = a(-2)^3 + b(-2)^2 + c(-2) + d = -8a + 4b - 2c + d = -4`

`` `f(x) = (x+2)(ex^2 + fx + g) - 4`

Since the problem does not provide at least three more informations about polynomial at specific values of x, the coefficients a,b,c,d that define the third degree polynomial remain unknown.

Hence, the third degree polynomial is `f(x)=ax^3 + bx^2 + cx + d`  whose coefficients check the relation  `-8a + 4b - 2c + d = -4` , under the given constraints.