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4.3: Real Zeroes of Polynomials Functions February 13, 2008

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Objectives Divide polynomials Understand the division algorithm, remainder theorem, and factor theorem Factor higher degree polynomials Analyze polynomials with multiple zeroes Find rational zeros Solve polynomial equations

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Divide polynomials Divide by a monomial (3x 3 +6x 2 +7)/(2x) Dividing by binomials or higher (2x 3 +4x 2 -x+6)/(x+1)

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Understand the division algorithm, remainder theorem, and factor theorem Division algorithm: f(x) = d(x) * q(x) + r(x) Remainder theorem if f(x) is divided by x-k, the remainder is f(k) Factor theorem f(x) has x-k as a factor if and only if f(k)=0

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Ways to factor polynomials functions Graphically– see where the zeros are Using synthetic algebra– if you know one zero (k), factor out x-k Factor out x if possible

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If you know the zeros f(x)= a(x-c 1 )(x-c 2 )… etc f(x)= 2x 2 -25x+77 Zeros 11/2 and 7

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Your assignment Page 288-292 –16-22 even –36, 38

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