Dividing Polynomials (SYNTHETIC Division)

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Presentation transcript:

Dividing Polynomials (SYNTHETIC Division) NOTES 6.3 B Dividing Polynomials (SYNTHETIC Division)

EX – Synthetic division (5x³ -13x² +10x -8) / (x-2) Opposite of number in divisor 2 5 -13 10 -8 10 -6 8 5 -3 4 5x² -3x + 4

EX – Synthetic division (3x³ -4x² +2x -1) / (x+1) Opposite of number in divisor -1 3 -4 2 -1 -3 +7 -9 3 -7 9 -10 3x2 -7x + 9 R-10

A Couple of Notes Use synthetic division when the coefficient in front of x is 1 (x- 2) (2x-3) YES NO

The Remainder Theorem If a polynomial f(x) is divided by (x - a), the remainder is the constant f(a).

The Remainder Theorem Example # 1 Find the remainder: (x2 + 3x - 12) / (x - 4) (4)2 + 3(4) – 12 = 16 + 12 - 12 = 16  R 16

The Remainder Theorem Example # 2 Find the remainder: (x4 – 5x2 + 4x + 12) / (x + 4) (-4)4 - 5(-4)2 + 4(-4) + 12 = 256 – 80 – 16 + 12 = 172  R172