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

1 Answer
Jul 24, 2015

Answer:

#color(red)((3x^3+2x^2+6x-2)/(x+2) = 3x^2-4x+14-30/(x+2))#

Explanation:

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

1

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

2

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

3

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

4

Step 5. Add down the column.

5

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

6

The quotient is #3x^2-4x+14 -30/(x+2)#.

Check:

#(x+2)( 3x^2-4x+14 -30/(x+2)) = (x+2)( 3x^2-4x+14) -30 =3x^3-4x^2+14x+6x^2-8x+28 -30 = 3x^3+2x^2+6x-2#