12 13 Multiple Choice 5 points f(x)=-4x g(x)=x^2-4 Find f(x)cdot g(x) -4x^3+16x 12x^2-23x+10 4x^3-5x^2+8x-10 12x^2+16x+4 Multiple Choice 5 points g(x)=4x-1 f(x)=3x-3 Find (fcdot g)(x) 12x^2+15x+3 4x^2-21x+5 -2x^3+3x^2-6x+9 12x^2-15x+3 Clear my selection

To solve these problems, we need to find the product of the given functions for each question.<br /><br />**First Question:**<br /><br />Given:<br />- \( f(x) = -4x \)<br />- \( g(x) = x^2 - 4 \)<br /><br />We need to find \( f(x) \cdot g(x) \).<br /><br />Calculate:<br />\[ f(x) \cdot g(x) = (-4x) \cdot (x^2 - 4) \]<br /><br />Distribute \(-4x\) across the terms in \(g(x)\):<br />\[ = -4x \cdot x^2 + (-4x) \cdot (-4) \]<br />\[ = -4x^3 + 16x \]<br /><br />The correct answer is:<br />- \(-4x^3 + 16x\)<br /><br />**Second Question:**<br /><br />Given:<br />- \( g(x) = 4x - 1 \)<br />- \( f(x) = 3x - 3 \)<br /><br />We need to find \((f \cdot g)(x)\).<br /><br />Calculate:<br />\[ (f \cdot g)(x) = (3x - 3) \cdot (4x - 1) \]<br /><br />Use the distributive property (FOIL method):<br />\[ = 3x \cdot 4x + 3x \cdot (-1) + (-3) \cdot 4x + (-3) \cdot (-1) \]<br />\[ = 12x^2 - 3x - 12x + 3 \]<br />\[ = 12x^2 - 15x + 3 \]<br /><br />The correct answer is:<br />- \(12x^2 - 15x + 3\)