question
given that $f(x) = x^2 - 5x - 24$ and $g(x) = x - 8$, find $f(x) \cdot g(x)$ and express the result as a polynomial in simplest form.

answer
attempt 1 out of 2

Question

question
given that $f(x) = x^2 - 5x - 24$ and $g(x) = x - 8$, find $f(x) \cdot g(x)$ and express the result as a polynomial in simplest form.

answer
attempt 1 out of 2

Accepted Answer

# Explanation:
## Step1: Apply distributive property (FOIL)
Multiply each term in $ f(x) = x^2 - 5x - 24 $ by each term in $ g(x) = x - 8 $:
$$
\begin{align*}
f(x)\cdot g(x)&=(x^2 - 5x - 24)(x - 8)\
&=x^2\cdot x + x^2\cdot(-8) - 5x\cdot x - 5x\cdot(-8) - 24\cdot x - 24\cdot(-8)
\end{align*}
$$
## Step2: Simplify each term
Simplify the products:
$$
\begin{align*}
&=x^3 - 8x^2 - 5x^2 + 40x - 24x + 192
\end{align*}
$$
## Step3: Combine like terms
Combine the $ x^2 $ terms and the $ x $ terms:
$$
\begin{align*}
&=x^3 + (-8x^2 - 5x^2) + (40x - 24x) + 192\
&=x^3 - 13x^2 + 16x + 192
\end{align*}
$$
# Answer:
$ x^3 - 13x^2 + 16x + 192 $

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QUESTION IMAGE

Question

Explanation:

Step1: Apply distributive property (FOIL)

Step2: Simplify each term

Step3: Combine like terms

Answer: