Zeros and multiplicities

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-4 multiplicity 2, -8 multiplicity 3, 5 multiplicity 1

Tags

CCSS.HSF-IF.C.7C

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Which root has a multiplicity of 2 in the graph?

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-3

Tags

CCSS.HSF-IF.C.7C

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2

Tags

CCSS.HSF-IF.C.7C

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-2 multiplicity 10, 12 multiplicity 9

Tags

CCSS.HSF-IF.C.7C

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Write a function rule for a polynomial with zeros at -1, 2, and 7 (all multiplicity of 1).

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Tags

CCSS.HSF-IF.C.7C

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Define 'zero' in the context of polynomial functions.

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A zero of a polynomial function is a value of x for which the function evaluates to zero.

Tags

CCSS.HSF-IF.C.7C

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What does 'multiplicity' mean in relation to zeros of a polynomial?

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Multiplicity refers to the number of times a particular zero is repeated in a polynomial.

Tags

CCSS.HSF-IF.C.7C

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How does the multiplicity of a zero affect the graph of a polynomial function?

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A zero with odd multiplicity crosses the x-axis, while a zero with even multiplicity touches the x-axis but does not cross it.

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What is the relationship between the degree of a polynomial and its zeros?

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The degree of a polynomial is equal to the total number of zeros, counting multiplicities.

Tags

CCSS.HSF-IF.C.7C

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If a polynomial has a zero at x = 3 with multiplicity 4, what does this imply about the graph at x = 3?

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The graph will touch the x-axis at x = 3 and will not cross it.