Question

For the polynomial below, -1 is a zero,h(x)= x^3 + x^2 - 9x -9Express h (x) as a product of linear factors.

Answer 1

So given that -1 is a zero, we can say that a factor of the polynomial is x+1.

Then,

$\begin{gathered} h(x)=x^3+x^2-9x-9 \\ h(x)=x^2(x+1)-9(x+1) \\ h(x)=(x+1)(x^2-9) \\ h(x)=(x+1)(x+3)(x-3) \end{gathered}$

Therefore,

h(x) = (x+1)(x+3)(x-3)