Select the correct answer. Function \( h \) is the product of functions \( f \) and \( g \). \( f(x)=3 x+2 \) \( g(x)=5 x-8 \) Which equation defines function \( h \) ? \( \begin{array}{l}\text { ? } h(x)=15 x^{2}-6 x-16 \\ h(x)=15 x-16 \\ h(x)=15 x^{2}-16 \\ h(x)=15 x^{2}-14 x-16\end{array} \)

To find function \( h \), which is the product of functions \( f \) and \( g \), we can use the expressions for \( f \) and \( g \). We have: \[ h(x) = f(x) \cdot g(x) = (3x + 2)(5x - 8) \] Now, expanding this: \[ h(x) = 15x^2 - 24x + 10 - 16 \] Combining terms gives us: \[ h(x) = 15x^2 - 14x - 16 \] Thus, the correct answer is \( h(x) = 15x^2 - 14x - 16 \). --- In the late 19th century, the notion of multiplying functions like \( f \) and \( g \) became more popular with the advent of calculus and algebraic manipulations. This paved the way for advanced mathematics, allowing mathematicians to explore product functions more deeply, leading to developments in physics and engineering. Analytical skills are crucial! A common mistake when multiplying polynomials is forgetting to combine like terms correctly. Be cautious with signs during expansion—it's easy to misplace a minus! Always double-check your calculations and perhaps use a visual aid like a grid to ensure you cover every combination!