Mustafa Gorham
4.3
Question 2, 4.3.7
HW Score: $85 \%, 8.5$ of 10 points
Points: 0 of 1
Use long division to find the quotient $Q(x)$ and the remainder $R(x)$ when $P(x)$ is divided by $d(x)$ and express $P(x)$ in the form $d(x) \cdot Q(x)+R(x)$.
\[
\begin{array}{l}
P(x)=x^{3}+2 x^{2}-62 x+180 \\
d(x)=x+10
\end{array}
\]
\[
P(x)=(x+10)
\]

Step 1 ：Given the polynomials P(x) and d(x) as follows:

Step 2 ：\(P(x) = x^{3} + 2x^{2} - 62x + 180\)

Step 3 ：\(d(x) = x + 10\)

Step 4 ：We are asked to perform polynomial long division on P(x) and d(x). The result of this division will be a quotient Q(x) and a remainder R(x), such that \(P(x) = d(x) \cdot Q(x) + R(x)\).

Step 5 ：Performing the division, we find the quotient Q(x) and the remainder R(x).

Step 6 ：Finally, we substitute these values into the equation to express P(x) in the form \(d(x) \cdot Q(x) + R(x)\).

Step 7 ：The final answer is the expression for P(x) in the form \(d(x) \cdot Q(x) + R(x)\), which is obtained by substituting the values of Q(x) and R(x) found from the division.