# How do you use synthetic division to divide 3x^3 + 2x^2 + 6x - 2 by x+2?

Jul 24, 2015

$\textcolor{red}{\frac{3 {x}^{3} + 2 {x}^{2} + 6 x - 2}{x + 2} = 3 {x}^{2} - 4 x + 14 - \frac{30}{x + 2}}$

#### Explanation:

Step 1. Write only the coefficients of $x$ in the dividend inside an upside-down division symbol.

Step 2. Change the sign of the constant in the divisor and put it at the left.

Step 3. Drop the first coefficient of the dividend below the division symbol.

Step 4. Multiply the drop-down by the divisor, and put the result in the next column.

Step 5. Add down the column.

Step 6. Repeat Steps 4 and 5 until you can go no farther

The quotient is $3 {x}^{2} - 4 x + 14 - \frac{30}{x + 2}$.

Check:

$\left(x + 2\right) \left(3 {x}^{2} - 4 x + 14 - \frac{30}{x + 2}\right) = \left(x + 2\right) \left(3 {x}^{2} - 4 x + 14\right) - 30 = 3 {x}^{3} - 4 {x}^{2} + 14 x + 6 {x}^{2} - 8 x + 28 - 30 = 3 {x}^{3} + 2 {x}^{2} + 6 x - 2$