Answer:
[tex](f\cdot g)(x) = 2x^3 + 5x^2-x-6[/tex]
Step-by-step explanation:
We are given the two functions:
[tex]f(x)=2x^2+x-3\text{ and } g(x)=x+2[/tex]
And we want to find:
[tex](f \cdot g)(x)[/tex]
Recall that this is equivalent to:
[tex]=f(x)\cdot g(x)[/tex]
Substitute. Hence:
[tex](f\cdot g)(x)= (2x^2+x-3)(x+2)[/tex]
Expand if desired:
[tex]\displaystyle = x(2x^2+x-3)+2(2x^2+x-3) \\ \\ = (2x^3+x^2-3x)+(4x^2+2x-6) \\ \\\ = 2x^3 + 5x^2-x-6[/tex]
