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Section 2.3 Polynomial and Synthetic Division

Section 2.3 Polynomial and Synthetic Division. Long Division of polynomials Ex. (6x 3 -19x 2 +16x-4) divided by (x-2) Ex. (x 3 -1) divided by (x-1) Ex (2x 4 +4x 3 -5x 2 +3x-2) divided by (x 2 + 2x-3). Synthetic Division. Works when dividing by a binomial of the form ( x-k )

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Section 2.3 Polynomial and Synthetic Division

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  1. Section 2.3 Polynomial and Synthetic Division Long Division of polynomials Ex. (6x3-19x2+16x-4) divided by (x-2) Ex. (x3-1) divided by (x-1) Ex (2x4+4x3-5x2+3x-2) divided by (x2+ 2x-3)

  2. Synthetic Division • Works when dividing by a binomial of the form (x-k) • Use for examples on first slide: • Ex. (6x3-19x2+16x-4) divided by (x-2) • Ex. (x3-1) divided by (x-1) • Ex (2x4+4x3-5x2+3x-2) divided by (x2+ 2x-3) • Write answer as a polynomial

  3. The Remainder Theorem • If a polynomial f(x) is divided by (x-k), then the remainder is r; r=f(k). • f(x)=3x3+8x2+5x-7; what is f(-2)? • f(-2)=-9, so (-2,-9) is on the graph

  4. The factor Theorem • A polynomial f(x) has a factor (x-k) iff f(k)=0. • Is (x-2) a factor of f(x)=2x4+7x3-4x2-27x-18 ? synthetically divide the remaining polynomial • Is (x+3) a factor of f(x)=2x4+7x3-4x2-27x-18 ? • Completely factor 2x4+7x3-4x2-27x-18 and find the four zeros.

  5. Using the remainder • r = f(k) • If r=0, then (x-k) is a factor of f(x) • If r=0, then (k,0) is an x-intercept of the graph of f

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