Question

determine the resulting polynomial:
$f(x) = 7x + 3$
$g(x) = -10x^2 + x + 5$
find: $f(x) \cdot g(x)$
answer
attempt 1 out of 2

Explanation:

Step1: Apply Distributive Property

Multiply each term in \( f(x) = 7x + 3 \) by each term in \( g(x)=-10x^{2}+x + 5 \).

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Step2: Simplify Each Product

Simplify each term using the rule \( a^{m}\cdot a^{n}=a^{m + n} \):

• \( 7x\cdot(-10x^{2})=-70x^{3} \)
• \( 7x\cdot x = 7x^{2} \)
• \( 7x\cdot5 = 35x \)
• \( 3\cdot(-10x^{2})=-30x^{2} \)
• \( 3\cdot x=3x \)
• \( 3\cdot5 = 15 \)

So we have:

$$ -70x^{3}+7x^{2}+35x-30x^{2}+3x + 15 $$

Step3: Combine Like Terms

Combine the \( x^{2} \) terms (\( 7x^{2}-30x^{2}=-23x^{2} \)) and the \( x \) terms (\( 35x + 3x=38x \)):

$$ -70x^{3}-23x^{2}+38x + 15 $$

Answer:

\( -70x^{3}-23x^{2}+38x + 15 \)