A.4 Polynomial Division a) Long division b) Synthetic Division
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A.4 Polynomial Division a) Long division b) Synthetic Division
1. Long Division - Review
169427
Division Algorithm
9427RemainderDivisor QuotientDividend = x
58916 x 3+
+
2. Polynomial DivisionUse long division to solve:
)3()2110( 2 xxx• Write in standard
form if not already
• Put in place holders (zeros) for missing terms.
2. Polynomial Division
)23()654( 32 xxxx
Write result as: Dividend = (Quotient)(Divisor) + Remainder
More Polynomial Division
(6x 3 10x 2 3x 5)(2x 2 1)
More Polynomial Division
(x 5 5x 3 10)(x 1)
3. Synthetic Division
)3()554( 23 xxxxSynthetic Division can be used ONLY when divisor is of form: x – c
Synthetic DivisionIf divisor is (x + c) use “-c” in the box
)2()124( 23 xxx
Synthetic DivisionUse synthetic division to perform the indicated operation.
(7x 3 17x 2 15x 9)(x 3)
4. Determine if divisor is a factorRecall the division algorithm:
RemainderDivisor QuotientDividend = x +
Is (x-3) a factor of ?
If the remainder is zero when we perform polynomial division, then the divisor is a factor
IMPORTANT:
)915177( 23 xxx
3x 962 xx1. Is a factor of ?
2. Is a factor of ?
12 x
4. Determine if divisor is a factor
4343 23 xxx