What is the value of k if x3 + kx2 + 7x + 5 is divided by x + 6 and gives a remainder of −1?

What is the value of k if x3 + kx2 + 7x + 5 is divided by x + 6 and gives a remainder of −1?

I am going to use remainder theorum.  :)

Here is one of many references for it if you want to take a look.

https://www.mathsisfun.com/algebra/polynomials-remainder-factor.html

\(f(x)=x^3+kx^2+7x+5\\ f(-6)=(-6)^3+k*(-6)^2+7*(-6)+5\\ f(-6)=-216+36k-42+5\\ f(-6)=-253+36k\\ But\;\;f(-6)=-1\\ -1=-253+36k\\ 252=36k\\ k=7\)

What is the value of k if x3 + kx2 + 7x + 5 is divided by x + 6 and gives a remainder of −1?

[ x^3 + kx^2 + 7x + 5] / [ x + 6] = -1

x=1   and   k= -20, or

x=2   and   k=-8.75, or

x=3   and   k= -6 8/9

Very nice, Melody  !!!!

Thanks Chris  :))