# 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?

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### 1 Answer

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.**