Question

9r² + 32r + 21
overline{quadquadquadquadquadquadquadquad}
r + 3
use long division.
9r + 5 + \frac{6}{r + 3}
9r + 5 - \frac{6}{r + 3}
9r - 5 - \frac{6}{r + 3}
9r - 5 + \frac{6}{r + 3}

Explanation:

Step1: Divide leading terms

$\frac{9r^2}{r}=9r$

Step2: Multiply divisor by $9r$

$9r(r+3)=9r^2+27r$

Step3: Subtract from dividend

$(9r^2+32r+21)-(9r^2+27r)=5r+21$

Step4: Divide new leading terms

$\frac{5r}{r}=5$

Step5: Multiply divisor by $5$

$5(r+3)=5r+15$

Step6: Subtract to find remainder

$(5r+21)-(5r+15)=6$

Step7: Write final expression

Quotient + $\frac{\text{Remainder}}{\text{Divisor}}$

Answer:

A. $9r + 5 + \frac{6}{r + 3}$