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Rationals- Synthetic Division

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POLYNOMIAL DIVISION, FACTORS AND REMAINDERS Synthetic division is an alternative method to dividing rationals. The great thing about synthetic division is that it does not require factoring. BACK

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First divide 3 into 6 or x into x 2 Now divide 3 into 5 or x into 11x Long Division If the divisor has more than one term, perform long division. You do the same steps with polynomial division as with integers. Let's do two problems, one with integers you know how to do and one with polynomials and copy the steps. 32 698x - 3 x 2 + 8x - 5 2 x 64 x 2 – 3x Now multiply by the divisor and put the answer below. Subtract (which changes the sign of each term in the polynomial) 5 11x Bring down the next number or term 8 - 5 1 + 11 Multiply and put below 32 11x - 33 subtract 26 28 This is the remainder Remainder added here over divisor

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Divide y into -2yDivide y into y 2 Let's Try Another One If any powers of terms are missing you should write them in with zeros in front to keep all of your columns straight. y + 2 y 2 + 0y + 8 y y 2 + 2y Subtract (which changes the sign of each term in the polynomial) -2y+ 8 - 2 Multiply and put below - 2y - 4 subtract 12 This is the remainder Remainder added here over divisor Write out with long division including 0y for missing term Bring down the next term Multiply and put below

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_ 0 Example #1 BACK

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Place Holders Every number in the divisor needs to have a place value holder starting from the highest degree and including a coefficient at the end. Just like the number 101 has a zero in the tens place to indicate that there are no tens in 101.

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4 Example #3 BACK

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16 You try!! BACK

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Rationals- Synthetic Division BACK

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