Synthetic division

Question

use synthetic division to perform the division

(-6x3+1/2x2-1/8)/(x+1/2)

Answer 1

(-6x³ + 1/2 x² - 1/8) / (x + 1/2)

 

To set up synthetic division, you divide by the number being subtracted from x, which would be -1/2.

Then, you write down the coefficients of the polynomial that you are dividing into, replacing missing terms with a zero.

 

-1/2l -6     1/2     0     -1/8

 

        ____  3      -7/4    7/8

         -6   7/2    -7/4     6/8

 

Bring down the -6, multiply -6 by -1/2

Add 3 + 1/2, which equals 7/2 as an improper fraction

Multiply 7/2 times -1/2, add 0 + -7/4

Multiply -7/4 by -1/2, add -1/8 and 7/8

Reduce 6/8 to 3/4

 

Now write your answer as a polynomial beginning with x², which is one degree less than your original polynomial. The number in the bottom row become the coefficients of your new polynomial.

 

-6x² + 7/2 x - 7/4  Remainder = 3/4