Answer:
[tex]k=-9[/tex]
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:
[tex]f(x)=x^2+kx+11[/tex]
And it is divided by the binomial:
[tex]x+1[/tex]
The remainder is 21.
Rewriting the divisor yields:
[tex]x-(-1)[/tex]
So, a = -1.
Then by the PRT:
[tex]f(-1)=(-1)^2+k(-1)+11=21[/tex]
Simplify:
[tex]1-k+11=21[/tex]
Solve for k:
[tex]k=-9[/tex]
