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