Question

$(x^{2}-3x-7)div(x+2)$

Explanation:

Step1: Rewrite using polynomial long division

We divide $x^2 - 3x - 7$ by $x+2$. First, divide the leading term of the dividend by the leading term of the divisor: $\frac{x^2}{x}=x$.

Step2: Multiply divisor by $x$

$x(x+2)=x^2 + 2x$

Step3: Subtract from dividend

$(x^2 - 3x - 7)-(x^2 + 2x)=-5x -7$

Step4: Divide new leading term

$\frac{-5x}{x}=-5$

Step5: Multiply divisor by $-5$

$-5(x+2)=-5x -10$

Step6: Subtract to find remainder

$(-5x -7)-(-5x -10)=3$

Step7: Write final expression

Combine the quotient and remainder: $x - 5 + \frac{3}{x+2}$

Answer:

$x - 5 + \frac{3}{x+2}$
(The select boxes correspond to: first box $x$, second box $5$, third box $3$, fourth box $x+2$)