How do you find the value of k so that the remainder is zero given $(x^3+4x^2-kx+1)div(x+1)$ ?

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Answer 1 · 2017-01-01T11:24:24

$k = -4$

$f(x) = x^3+4x^2-kx+1$

By the remainder theorem, the remainder when dividing a polynomial $f(x)$ by $(x-a)$ is $f(a)$

In our case, we have $a=-1$ and we need:

$0 = f(-1) = (-1)^3+4(-1)^2-k(-1)+1$

$color(white)(0 = f(-1)) = -1+4+k+1$

$color(white)(0 = f(-1)) = k+4$

Hence $k = -4$

How do you find the value of k so that the remainder is zero given (x^3+4x^2-kx+1)div(x+1)(x^3+4x^2-kx+1)div(x+1)?