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College Algebra / Unit 7   Alg 356 short lesson, about 20 seconds

Zeros and Multiplicity

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The idea

A zero's multiplicity is its factor's exponent in the factored form; the graph crosses the x-axis at odd multiplicity and touches without crossing at even.

In practice

f(x) = (x − 1)²(x + 2): at 1 the square makes it touch and turn; at −2 the single factor makes it cross.

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