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

Divide $x^2 - 4x - 3$ by $x+1$. First term: $\frac{x^2}{x}=x$. Multiply $d(x)$ by $x$: $x(x+1)=x^2+x$. Subtract from $f(x)$:
$(x^2 - 4x - 3)-(x^2+x)=-5x-3$

Step2: Find next term of quotient

Next term: $\frac{-5x}{x}=-5$. Multiply $d(x)$ by $-5$: $-5(x+1)=-5x-5$. Subtract from remainder:
$(-5x-3)-(-5x-5)=2$

Step3: Identify remainder

The remainder $R(x)$ is the constant value left.

Answer:

$2$