Mustafa Gorham
4.3
Question 2, 4.3.7
HW Score: $85\mathrm{\%},8.5$ 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 $d(x)\cdot Q(x)+R(x)$.
$$\begin{array}{l}P(x)=x^3+2x^2-62x+180\\ d(x)=x+10\end{array}$$
$$P(x)=(x+10)$$

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.