Question

Given that (x+8) is a factor of f(x)=x^3+4x^2+6x+k,what is the value of k

Answer 1

`f(x)=x^3+4x^2+6x+k`

If x+8 is a factor then it follows that;

x + 8 = 0

x = - 8

Substituting -8 for x in the function and equating f(x) to zero, we have,

`\begin{gathered} (-8)^3+4(-8)^2+6(-8)+k=0 \\ -512+256-48+k=0 \\ -560+256+k=0 \\ k=560-256 \\ k=304 \end{gathered}`

The solution is; the value of k is 304