algebra 2
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dividing polynomials
divide.
1) $(n^3 - 10n^2 + 26n - 8) ÷ (n - 4)$
n - 4 \overline{\smash{)} -10n^2 + 26n - 8}

Question

Accepted Answer

# Explanation:
## Step1: Use polynomial long division. Divide the first term of the dividend $n^3 - 10n^2 + 26n - 8$ by the first term of the divisor $n - 4$, which is $n$. Multiply the divisor by $n^2$ to get $n^3 - 4n^2$. Subtract this from the dividend:
$$
\begin{align*}
&(n^3 - 10n^2 + 26n - 8) - (n^3 - 4n^2)\
=&n^3 - 10n^2 + 26n - 8 - n^3 + 4n^2\
=& -6n^2 + 26n - 8
\end{align*}
$$
## Step2: Now, divide the first term of $-6n^2 + 26n - 8$ (which is $-6n^2$) by $n$ (the first term of the divisor), getting $-6n$. Multiply the divisor by $-6n$ to get $-6n^2 + 24n$. Subtract this from $-6n^2 + 26n - 8$:
$$
\begin{align*}
&(-6n^2 + 26n - 8) - (-6n^2 + 24n)\
=& -6n^2 + 26n - 8 + 6n^2 - 24n\
=& 2n - 8
\end{align*}
$$
## Step3: Divide the first term of $2n - 8$ (which is $2n$) by $n$, getting $2$. Multiply the divisor by $2$ to get $2n - 8$. Subtract this from $2n - 8$:
$$
(2n - 8) - (2n - 8) = 0
$$
## Step4: Combine the results from each step. The quotient is $n^2 - 6n + 2$ and the remainder is $0$. So, $(n^3 - 10n^2 + 26n - 8) \div (n - 4)=n^2 - 6n + 2$.
# Answer:
$n^2 - 6n + 2$

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Question

Explanation:

Step1: Use polynomial long division. Divide the first term of the dividend \(n^3 - 10n^2 + 26n - 8\) by the first term of the divisor \(n - 4\), which is \(n\). Multiply the divisor by \(n^2\) to get \(n^3 - 4n^2\). Subtract this from the dividend:

Step2: Now, divide the first term of \(-6n^2 + 26n - 8\) (which is \(-6n^2\)) by \(n\) (the first term of the divisor), getting \(-6n\). Multiply the divisor by \(-6n\) to get \(-6n^2 + 24n\). Subtract this from \(-6n^2 + 26n - 8\):

Step3: Divide the first term of \(2n - 8\) (which is \(2n\)) by \(n\), getting \(2\). Multiply the divisor by \(2\) to get \(2n - 8\). Subtract this from \(2n - 8\):

Step4: Combine the results from each step. The quotient is \(n^2 - 6n + 2\) and the remainder is \(0\). So, \((n^3 - 10n^2 + 26n - 8) \div (n - 4)=n^2 - 6n + 2\).

Answer: