Question

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

Answer 1

Answer:

$k=-9$

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:

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

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:

$k=-9$