Dividing Polynomials Long Division A little review:

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Presentation transcript:

Dividing Polynomials Long Division A little review: Ex 1: Factor completely. Ex 2: Divide

Division Algorithm f (x) = d (x) q (x) +r (x) where f (x) is the dividend, d (x) is the divisor, q (x) is the quotient, and r (x) is the remainder. Ex 3: Divide: Ex 4: Divide:

Synthetic Division Ex 5: Ex 6:

The Remainder Theorem If the polynomial f (x) is divided by x - k, then the remainder is the value of f (k). Ex 7: Evaluate P (-4) for P(x) = x4 - 5x2 + 4x + 12. Ex 8: Evaluate P (-1) for P(x) = 2x4 + 6x3 - 5x2 - 59.

The Factor Theorem A polynomial f (x) has a factor x – k if and only if f (k) = 0. Ex 9: Show that (x – 2) and (x + 3) are factors of f (x) = 2x4 + 7x3 - 4x2 – 27x – 18. They are both factors of f (x) since f (2) and f (-3) both equal 0.

Practice Assignment: Section 2.3A (pg 123 - 124) #1-44