Question

determine the resulting polynomial:

$f(x) = 4x + 2$

$g(x) = 10x^2 + 9x - 10$

find: $f(x) \cdot g(x)$

answer
attempt 1 out of 2

Explanation:

Step1: Apply distributive property

Multiply each term in \( f(x) = 4x + 2 \) by each term in \( g(x)=10x^{2}+9x - 10 \).

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Step2: Simplify each product

Calculate each term:

• \( 4x\cdot(10x^{2}) = 40x^{3} \)
• \( 4x\cdot(9x)=36x^{2} \)
• \( 4x\cdot(-10)=-40x \)
• \( 2\cdot(10x^{2}) = 20x^{2} \)
• \( 2\cdot(9x)=18x \)
• \( 2\cdot(-10)=-20 \)

So we have \( 40x^{3}+36x^{2}-40x + 20x^{2}+18x-20 \)

Step3: Combine like terms

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

• For \( x^{2} \) terms: \( 36x^{2}+20x^{2}=56x^{2} \)
• For \( x \) terms: \( - 40x+18x=-22x \)

Putting it all together, we get \( 40x^{3}+56x^{2}-22x - 20 \)

Answer:

\( 40x^{3}+56x^{2}-22x - 20 \)