Functions find (f⋅g)(x) and (f⋅g)(0)

Question

For the functions f(x)=x^2−x+3 and g(x)=3x^2−10x−5, find (f⋅g)(x) and (f⋅g)(0).

Answer 1

$f(x)=x^2-3x+3$

$g(x)=3x^2-10x+5$

(f*g)(x) means to multiply f(x) by g(x):

($f\ast g)(x)=(x^2-3x+3)(3x^2-10x-5)$

FOIL it out to get the answer. Be sure to combine like terms after you FOIL it. You will end up with a 5 term degree 4 polynomial. To evaluate (f*g)(0), just plug in x=0 and compute the answer. All the x terms will go to zero leaving you with the constant term, -15.