Question

determine the resulting polynomial:
$f(x) = 9x + 4$
$g(x) = -4x^2 - 9x + 5$
find: $f(x) \cdot g(x)$
answer
attempt 1 out of 2
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Explanation:

Step1: Apply distributive property (FOIL for polynomials)

Multiply each term in \( f(x) = 9x + 4 \) by each term in \( g(x)=-4x^{2}-9x + 5 \).

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Step2: Simplify each product

Calculate each term:

• \( 9x\cdot(-4x^{2})=-36x^{3} \)
• \( 9x\cdot(-9x)=-81x^{2} \)
• \( 9x\cdot5 = 45x \)
• \( 4\cdot(-4x^{2})=-16x^{2} \)
• \( 4\cdot(-9x)=-36x \)
• \( 4\cdot5 = 20 \)

Step3: Combine like terms

Combine the \( x^{2} \) terms and the \( x \) terms:

• For \( x^{2} \): \( -81x^{2}-16x^{2}=-97x^{2} \)
• For \( x \): \( 45x-36x = 9x \)

Now, put all terms together: \( -36x^{3}-97x^{2}+9x + 20 \)

Answer:

\( -36x^{3}-97x^{2}+9x + 20 \)