Question

What is the remainder of f(x)=x^4-2x^3-27x^2-9x+18 when divided by binomial x+4

Answer 1

The remainder will be 6.

Explanation:

We have the function:

`f(x)=x^4-2x^3-27x^2-9x+18`

And we want to find the remainder after it is divided by the binomial:

`x+4`

We can use the Polynomial Remainder Theorem. According to the PRT, if we have a polynomial P(x) being divided by a binomial in the form (x - a), then the remainder will be given by P(a).

Here, our divisor is (x + 4). We can rewrite this as (x - (-4)).

Therefore, a = -4.

Then according to the PRT, the remainder will be:

`f(-4)=(-4)^4-2(-4)^3-27(-4)^2-9(-4)+18=6`

The remainder will be 6.