Question

select the correct answer.

function (h) is the product of functions (f) and (g).
(f(x) = -5x - 9)
(g(x) = 8x - 4)

which equation defines function (h)?

• (h(x) = -40x^2 - 52x + 36)
• (h(x) = -40x^2 + 36)
• (h(x) = -40x^2 - 13x + 36)
• (h(x) = -40x + 36)

Explanation:

⚡ Using what you learned: Operations with Polynomial Functions

Step 1: Set up the product function

$$ h(x) = f(x) \cdot g(x) $$

$$ h(x) = (-5x - 9)(8x - 4) $$

Step 2: Multiply the binomials

$$ h(x) = (-5x)(8x) + (-5x)(-4) + (-9)(8x) + (-9)(-4) $$

$$ h(x) = -40x^2 + 20x - 72x + 36 $$

Step 3: Combine like terms

$$ h(x) = -40x^2 - 52x + 36 $$

Answer:

\( h(x) = -40x^2 - 52x + 36 \) (The first option)