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?

Step-by-step 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:

And it is divided by the binomial:

The remainder is 21.

Rewriting the divisor yields:

So, a = -1.

Then by the PRT:

Simplify:

Solve for k:

hope this .

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