Question

If (x+2) is a factor of h(x) = x^3 + 8x² + Ax + 4 , then valoe of A is:

Answer 1

If $x+2$ is a factor of $h(x)$, then by the polynomial remainder theorem, $h(-2)=0$. So

$h(-2)=(-2)^3+8(-2)^2+A(-2)+4$

$-8+32-2A+4=0\implies2A=28\implies A=14$