[tex]f(x)=x^2+2x-6\\\\g(x)=x^4+3[/tex]
[tex](f\cdot g)(x)=f(x)\cdot g(x)[/tex]
Use FOIL (a + b)(c + d) = ac + ad + bc + bd
[tex](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)[/tex]
Use [tex]a^n\cdot a^m=a^{n+m}[/tex]
[tex]=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}[/tex]
