What is a zero of a polynomial?
Roots & Multiplicity

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Mathematics
•
12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Back
A zero of a polynomial is a value of x that makes the polynomial equal to zero. It is also known as a root.
2.
FLASHCARD QUESTION
Front
Define multiplicity in the context of polynomial roots.
Back
Multiplicity refers to the number of times a particular root (zero) appears in a polynomial. For example, if (x - r) appears k times, then r has a multiplicity of k.
3.
FLASHCARD QUESTION
Front
What effect does an odd multiplicity have on the graph of a polynomial at its zero?
Back
An odd multiplicity means the graph will cross the x-axis at that zero.
4.
FLASHCARD QUESTION
Front
What effect does an even multiplicity have on the graph of a polynomial at its zero?
Back
An even multiplicity means the graph will touch the x-axis and turn around at that zero.
5.
FLASHCARD QUESTION
Front
Given the polynomial f(x) = (x + 5)^3(x - 9)^2(x + 2)(x - 4), list its zeros.
Back
The zeros are -5 (multiplicity 3), 9 (multiplicity 2), -2 (multiplicity 1), and 4 (multiplicity 1).
6.
FLASHCARD QUESTION
Front
How do you determine the multiplicity of a zero from a polynomial expression?
Back
The multiplicity of a zero can be determined by the exponent of the factor associated with that zero in the polynomial.
7.
FLASHCARD QUESTION
Front
What are the zeros of the polynomial y = 3(x + 4)(x + 1)(x - 3)?
Back
The zeros are -4, -1, and 3.
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