How do you use synthetic division to divide 3x^3 - x^2 + 8x-103x3−x2+8x−10 by x-1x−1?

1 Answer
Ernest Z.
Jul 24, 2015

color(red)((3x^3-x^2+8x-10)/(x-1) = 3x^2+2x+10)3x3−x2+8x−10x−1=3x2+2x+10

Explanation:

Step 1. Write only the coefficients of xx 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+2x+103x2+2x+10.

Check:

(x-1)( 3x^2+2x+10) = 3x^3+2x^2+10x-3x^2-2x-10 = 3x^3-x^2+8x-10(x−1)(3x2+2x+10)=3x3+2x2+10x−3x2−2x−10=3x3−x2+8x−10

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