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Synthetic Division Dela Peña, Kenneth A.

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

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Study The Example: 1. x 3 – x 2 + x – 1 divided by x – 1

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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

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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

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Step 3 : -Add the numbers in second column. 1 -1 └ 1 1 + 1 -1 + 1 = 0

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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 0 0 1 x 0 = = 1 + 0 1

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

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└ 1 1 -1 1 + 1 0 0 1x 2 + 0x 1 + 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 x 2 + 1 =

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