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