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Polynomial P(x)
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Binomial Factors
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Polynomial P(x) Binomial Factors Solutions of P(x)=0 Zeros of P(x)
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Polynomial P(x) Binomial Factors Solutions of P(x)=0 Zeros of P(x)
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If in polynomial P(x), P(c) = 0
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Zero P(x)=0
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Zero P(x)=0 Binomial Factors
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Polynomial P(x) Binomial Factors Solutions of P(x)=0 Zeros of P(x)
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Solutions of P(x)=0 Zeros of P(x)
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Solutions of P(x)=0 Zeros of P(x)
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Solutions of P(x)=0 Zeros of P(x)
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Zeros P(x)=0 The graph is tangent (touches) the x-axis but doesn’t cross the x-axis at that point
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Zeros P(x)=0 The graph is tangent (touches) the x-axis but doesn’t cross the x-axis at that point Binomial Factors
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P(x)=0
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P(x)=0
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P(x)=0
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P(x)=0
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1
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1
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1
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– 3, multiplicity 2 2, multiplicity 1
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– 3, multiplicity 2 2, multiplicity 1
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– 3, multiplicity 2 2, multiplicity 1
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x2x2 6x6x9 x –2
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x2x2 6x6x9 x
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x2x2 6x6x9 x
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Shifted 2 to the left
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The graph intersects the x-axis and flattens out as it passes through that point.
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If the degree of the binomial is odd and greater than 1, the graph will intersect the x-axis and flatten out as it passes through that point.
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If the degree of the binomial is odd and greater than 1, the graph will intersect the x-axis and flatten out as it passes through that point.
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–1 123
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123
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123
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123
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The graph is tangent (touches) the x-axis but doesn’t cross the x-axis at that point
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The graph is tangent (touches) the x-axis but doesn’t cross the x-axis at that point
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Example 1
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– 3
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2 nd TABLE
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Example 2
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ZOOM 1: ZBox
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Page 342: #34 and #37 Graphing Calculator
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