Question

Given f(x) = x2 + kx + 11, and the remainder when f(x) is divided by x + 1 is

21, then what is the value of k?

Answer 1

`k=-9`

Explanation:

According to the Polynomial Remainder Theorem, when dividing a polynomial P(x) by a binomial in the form (x - a), the remainder will be given by P(a).

We are given the polynomial:

`f(x)=x^2+kx+11`

And it is divided by the binomial:

`x+1`

The remainder is 21.

Rewriting the divisor yields:

`x-(-1)`

So, a = -1.

Then by the PRT:

`f(-1)=(-1)^2+k(-1)+11=21`

Simplify:

`1-k+11=21`

Solve for k:

`k=-9`