Question

What is (f·g)(x)?

f(x)=x^2+2x−6

g(x)=x^4+3

Answer 1

`f(x)=x^2+2x-6\\\\g(x)=x^4+3`

`(f\cdot g)(x)=f(x)\cdot g(x)`

Use FOIL (a + b)(c + d) = ac + ad + bc + bd

`(f\cdot g)(x)=(x^2+2x-6)(x^4+3)\\\\=(x^2)(x^4)+(x^2)(3)+(2x)(x^4)+(2x)(3)+(-6)(x^4)+(-6)(3)`

Use
`a^n\cdot a^m=a^(n+m)`

`=x^(2+4)+3x^2+2x^(1+4)+6x-6x^4-18\\\\=x^6+3x^2+2x^5+6x-6x^4-18\\\\\boxed{(f\cdot g)(x)=x^6+2x^5-6x^4+3x^2+6x-18}`