Questions: Divide. [ left(3 x^2+21 x+13right) div(x+6) ] Your answer should give the quotient and the Quotient: Remainder:

Transcript text: Divide. \[ \left(3 x^{2}+21 x+13\right) \div(x+6) \] Your answer should give the quotient and the Quotient: $\square$ Remainder: $\square$

Solution

Solution Steps

Step 1: Divide the Leading Terms

Divide $3 x^{2}$ by $x$, resulting in $3 x$. The remaining expression is $3 x + 13$.

Step 2: Continue Division

Next, divide $3 x$ by $x$, resulting in $3$. The remaining expression is $-5$.

Step 3: Combine Results

The quotient of the division is $3 x + 3$ and the remainder is $-5$. Thus, we can express the division as: \[ \frac{3 x^{2} + 21 x + 13}{x + 6} = 3 x + 3 - \frac{5}{x + 6} \]

Final Result

Quotient: $3 x + 3$
Remainder: $-5$