How do you determine the value of k if the remainder is 3 given $(x^3+kx^2+x+5) div(x+2)$ ?

Question

108530 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-13T15:39:03

The answer is $k=2$

Let $f(x)=x^3+kx^2+x+5$

When $f(x)$ is divided by $(x+2)$ , the remainder is $=3$

This is the remainder theorem

so,

$f(-2)=-8+4k-2+5=3$

$4k=3+5 =8$

$k=2$

How do you determine the value of k if the remainder is 3 given (x^3+kx^2+x+5) div(x+2)(x^3+kx^2+x+5) div(x+2)?