Question

divide f(x) by d(x). your answer should be in the following format:
\\(\frac{f(x)}{d(x)} = q(x) + \frac{r(x)}{d(x)}\\)

\\(f(x) = x^2 - 4x - 3\\) \\(d(x) = x + 1\\)

\\(r(x) = ?\\)

only enter the r(x) term.

Explanation:

Step1: Use polynomial long division or synthetic division. Let's use synthetic division. The root of \(d(x)=x + 1\) is \(x=-1\).

Set up synthetic division:
\[

$$\begin{array}{r|rrr} -1 & 1 & -4 & -3 \\ & & -1 & 5 \\ \hline & 1 & -5 & 2 \\ \end{array}$$

\]

Step2: The remainder \(R(x)\) is the last number in the synthetic division result, which is 2. Since the degree of the remainder is less than the degree of \(d(x)\) (which is 1), the remainder is a constant. So \(R(x)=2\).

Answer:

2