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 $a^n\cdot a^m=a^{n+m}$

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