Question

what is $h(x) = f(x) g(x)$?
$\circ\\ h(x) = -22x^2 + 34x + 20$
$\circ\\ h(x) = -22x^2 + 10x - 24$
$\circ\\ h(x) = 22x^2 - 54x + 20$
$\circ\\ h(x) = -22x^2 - 34x + 20$
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Explanation:

To solve for \( h(x) = f(x)g(x) \), we need to know the expressions for \( f(x) \) and \( g(x) \). Since they are not provided in the question, we can't directly compute \( h(x) \). However, if we assume a common scenario (e.g., \( f(x) \) and \( g(x) \) are linear functions like \( f(x) = -11x + 5 \) and \( g(x) = 2x + 4 \) or other combinations), let's check the options:

Looking at the leading coefficient of \( x^2 \) (which is the product of the leading coefficients of \( f(x) \) and \( g(x) \)):

• For option \( h(x) = -22x^2 + 34x + 20 \), the leading coefficient is \( -22 \), which could come from \( (-11) \times 2 \) or \( (11) \times (-2) \).
• For option \( h(x) = -22x^2 + 10x - 24 \), the constant term is \( -24 \), which would be the product of the constant terms of \( f(x) \) and \( g(x) \).
• For option \( h(x) = 22x^2 - 54x + 20 \), the leading coefficient is positive \( 22 \), so the leading coefficients of \( f(x) \) and \( g(x) \) would have the same sign.
• For option \( h(x) = -22x^2 - 34x + 20 \), the middle term is negative.

But without \( f(x) \) and \( g(x) \), we can't be sure. However, if we assume a common problem where \( f(x) = -11x + 5 \) and \( g(x) = 2x + 4 \), then:

\( f(x)g(x) = (-11x + 5)(2x + 4) = -22x^2 - 44x + 10x + 20 = -22x^2 - 34x + 20 \), which is option D. But if \( f(x) = -11x + 5 \) and \( g(x) = -2x + 4 \), then:

\( f(x)g(x) = (-11x + 5)(-2x + 4) = 22x^2 - 44x - 10x + 20 = 22x^2 - 54x + 20 \), which is option C.

Wait, maybe the original \( f(x) \) and \( g(x) \) are \( f(x) = -11x + 5 \) and \( g(x) = 2x + 4 \) (leading to option D) or \( f(x) = 11x - 5 \) and \( g(x) = -2x + 4 \) (leading to option C). But since the problem is incomplete, we need the expressions for \( f(x) \) and \( g(x) \).

Assuming a common problem where \( f(x) = -11x + 5 \) and \( g(x) = 2x + 4 \), then \( h(x) = -22x^2 - 34x + 20 \) (option D). But if \( f(x) = -11x + 5 \) and \( g(x) = -2x + 4 \), then \( h(x) = 22x^2 - 54x + 20 \) (option C).

However, since the problem is likely expecting a specific answer, and if we consider a common problem where \( f(x) = -11x + 5 \) and \( g(x) = 2x + 4 \), then the answer is:

Answer:

D. \( h(x) = -22x^2 - 34x + 20 \)

(Note: This answer is based on an assumed scenario. To get the correct answer, we need the expressions for \( f(x) \) and \( g(x) \).)