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. x 3 – x 2 + 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 x 3 x 2 x Constant 1 1 └ 1 This is b in x - b Bring down 1 x 3 – x 2 + x – 1 divided by x – 1

Step 2 : - Multiply the first numerical coefficient by b. Put the product below the next numerical coefficient └ x 1 = 1

Step 3 : -Add the numbers in second column └ = 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 └ x 0 = =

Step 5 : - Continue the process until the last column is filled └ x 1 = 1 0= remainder +

└ x 2 + 0x 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 x =