synthetic division dela peña, kenneth a.. - is a shorthand, or shortcut, method of dividing...

Synthetic Division

Dela Peña, Kenneth A.

- is a shorthand, or shortcut, method of dividing polynomial by a binomial of the form x – b.

•Synthetic Division

Study The Example:

1. x3 – x2 + x – 1 divided by x – 1

Step 1 : - Get the numerical

coefficients of each terms where must be arranged such that exponents are descending consecutively

x3 x2 x Constant

1 -1 1 -1 └1

This is b in x - b

Bring down

1

x3 – x2 + x – 1 divided by x – 1

Step 2 : - Multiply the first numerical

coefficient by b. Put the product below the next numerical coefficient.

1 -1 1 -1 └1

1

+

1 x 1

= 1

Step 3 : -Add the numbers in second column.

1 -1 1 -1 └1

1

+ 1

-1 + 1= 0

Step 4 : - Do step 2, this time

multiplying the sum of the second column by b and write the products below the next numerical coefficient in the next column.

1 -1 1 -1 └1

1

+ 1

0

0

1 x 0

=

= 1 + 01

Step 5 :- Continue the process

until the last column is filled.

1 -1 1 -1 └1

1

+ 1

0

0

1 1 x 1= 1

0=

remainder+

└1

1 -1 1 -1

1

+ 1

0

0

1x2 + 0x1 + 1

1

0

- This sums are the numerical coefficient of each term in quotient where the first is the numerical coefficient of the term x n – 1 .

1

x2 + 1=

-FIN-