Answer:
[tex]\large\boxed{f(x)\cdot g(x)=-12x^3-28x^2+30x-8}[/tex]
Step-by-step explanation:
[tex]f(x)=4x-2\\\\g(x)=-3x^2-7x+4\\\\f(x)\cdot g(x)=(4x-2)\cdot(-3x^2-7x+4)\\\\\text{Use FOIL}\ (a+b)(c+d)=ac+ad+bc+bd\\\\f(x)\cdot g(x)=(4x)(-3x^2)+(4x)(-7x)+(4x)(4)\\+(-2)(-3x^2)+(-2)(-7x)+(-2)(4)\\\\f(x)\cdot g(x)=-12x^3-28x^2+16x+6x^2+14x-8\\\\\text{Combine like terms}\\\\f(x)\cdot g(x)=-12x^3+(-28x^2+6x^2)+(16x+14x)-8\\\\f(x)\cdot g(x)=-12x^3-28x^2+30x-8[/tex]
