3) $(n^3 + n^2 + 8n + 20) div (n + 2)$

Question

Accepted Answer

# Explanation:
## Step 1: Use polynomial long division
Divide the first term of the dividend $n^3$ by the first term of the divisor $n$ to get $n^2$. Multiply the divisor $n + 2$ by $n^2$ to get $n^3 + 2n^2$. Subtract this from the dividend:
$$
\begin{align*}
&(n^3 + n^2 + 8n + 20) - (n^3 + 2n^2)\
=&n^3 + n^2 + 8n + 20 - n^3 - 2n^2\
=& -n^2 + 8n + 20
\end{align*}
$$
## Step 2: Divide the new first term $-n^2$ by $n$
We get $-n$. Multiply the divisor $n + 2$ by $-n$ to get $-n^2 - 2n$. Subtract this from the previous result:
$$
\begin{align*}
&(-n^2 + 8n + 20) - (-n^2 - 2n)\
=& -n^2 + 8n + 20 + n^2 + 2n\
=& 10n + 20
\end{align*}
$$
## Step 3: Divide the new first term $10n$ by $n$
We get $10$. Multiply the divisor $n + 2$ by $10$ to get $10n + 20$. Subtract this from the previous result:
$$
\begin{align*}
&(10n + 20) - (10n + 20)\
=& 10n + 20 - 10n - 20\
=& 0
\end{align*}
$$
## Step 4: Combine the results
The quotient is $n^2 - n + 10$ and the remainder is $0$. So, $(n^3 + n^2 + 8n + 20)\div(n + 2)=n^2 - n + 10$

# Answer:
$n^2 - n + 10$

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QUESTION IMAGE

Question

Explanation:

Step 1: Use polynomial long division

Step 2: Divide the new first term \(-n^2\) by \(n\)

Step 3: Divide the new first term \(10n\) by \(n\)

Step 4: Combine the results

Answer: