Product and Quotient Functions m(x)=x^2+4x (mn)(x)= x^2+4x(x) (x^2+4x)(x) COMPLITE Which is equal to: x^3+4x^2 5x^2 4x^4 COMPLETE n(x)=x Evaluate (mn)(x) for x=-3 (mn)(-3)=9 COMPLETE (m)/(n)(x),xneq

To find the product and quotient functions, we need to multiply and divide the given functions $m(x)$ and $n(x)$.<br /><br />Given:<br />$m(x) = x^2 + 4x$<br />$n(x) = x$<br /><br />Step 1: Find the product function $(mn)(x)$.<br />$(mn)(x) = m(x) \cdot n(x)$<br />$(mn)(x) = (x^2 + 4x) \cdot x$<br />$(mn)(x) = x^3 + 4x^2$<br /><br />Therefore, $(mn)(x)$ is equal to $x^3 + 4x^2$.<br /><br />Step 2: Evaluate $(mn)(x)$ for $x = -3$.<br />$(mn)(-3) = (-3)^3 + 4(-3)^2$<br />$(mn)(-3) = -27 + 36$<br />$(mn)(-3) = 9$<br /><br />Therefore, $(mn)(-3)$ is equal to 9.<br /><br />Step 3: Find the quotient function $\frac{m}{n}(x)$.<br />$\frac{m}{n}(x) = \frac{m(x)}{n(x)}$<br />$\frac{m}{n}(x) = \frac{x^2 + 4x}{x}$<br /><br />Since $x \neq 0$, we can simplify the expression:<br />$\frac{m}{n}(x) = x + 4$<br /><br />Therefore, $\frac{m}{n}(x)$ is equal to $x + 4$ when $x \neq 0$.