Question

If p(x) = 2x2 – 4x and q(x) = x – 3, what is (p*q)(x)

Answer 1

(p*q)(x) simply means p(x) * g(x)
which in this case will be \(\bf (2x^2-4x) \cdot (x-3)\)

Answer 2

Recall that:
\[(p*q)(x)=p(x)*q(x)\]
if
\[p(x)=2x^2-4x\]
\[g(x)=x-3\]
than:
\[[2x^2-4x][x-3]=2x^3-2x^2-4x^2+12x=2x^3-6x^2+12x\]
\[(p*q)(x)=2x^3-6x^2+12x\]