Polynomial P(x) Binomial Factors Polynomial P(x) Binomial Factors Solutions of P(x)=0 Zeros of P(x)

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Presentation transcript:

Polynomial P(x)

Binomial Factors

Polynomial P(x) Binomial Factors Solutions of P(x)=0 Zeros of P(x)

Polynomial P(x) Binomial Factors Solutions of P(x)=0 Zeros of P(x)

If in polynomial P(x), P(c) = 0

Zero P(x)=0

Zero P(x)=0 Binomial Factors

Polynomial P(x) Binomial Factors Solutions of P(x)=0 Zeros of P(x)

Solutions of P(x)=0 Zeros of P(x)

Solutions of P(x)=0 Zeros of P(x)

Solutions of P(x)=0 Zeros of P(x)

Zeros P(x)=0 The graph is tangent (touches) the x-axis but doesn’t cross the x-axis at that point

Zeros P(x)=0 The graph is tangent (touches) the x-axis but doesn’t cross the x-axis at that point Binomial Factors

P(x)=0

P(x)=0

P(x)=0

P(x)=0

1

1

1

– 3, multiplicity 2 2, multiplicity 1

– 3, multiplicity 2 2, multiplicity 1

– 3, multiplicity 2 2, multiplicity 1

x2x2 6x6x9 x –2

x2x2 6x6x9 x

x2x2 6x6x9 x

Shifted 2 to the left

The graph intersects the x-axis and flattens out as it passes through that point.

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.

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.

–1 123

123

123

123

The graph is tangent (touches) the x-axis but doesn’t cross the x-axis at that point

The graph is tangent (touches) the x-axis but doesn’t cross the x-axis at that point

Example 1

– 3

2 nd TABLE

Example 2

ZOOM 1: ZBox

Page 342: #34 and #37 Graphing Calculator