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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?

Sagot :

XKelvinidn

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]

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