
Graphs of Polynomial
Flashcard
•
Mathematics
•
9th - 12th Grade
•
Practice Problem
•
Hard
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a polynomial?
Back
A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, f(x) = 5x^4 + 2x^3 + 2x - 7 is a polynomial.
2.
FLASHCARD QUESTION
Front
What is the degree of a polynomial?
Back
The degree of a polynomial is the highest power of the variable in the polynomial. For example, in f(x) = 5x^4 + 2x^3 + 2x - 7, the degree is 4.
3.
FLASHCARD QUESTION
Front
How many solutions can a polynomial have?
Back
A polynomial of degree n can have at most n solutions (roots). For example, a polynomial of degree 4 can have at most 4 solutions.
4.
FLASHCARD QUESTION
Front
What is end behavior of a polynomial function?
Back
End behavior describes how the values of a polynomial function behave as x approaches positive or negative infinity. It is determined by the leading term of the polynomial.
5.
FLASHCARD QUESTION
Front
What does it mean for a polynomial to be factored?
Back
Factoring a polynomial means expressing it as a product of its factors. For example, f(x) = (x-5)^2(x-2)(x+3) is a factored form of a polynomial.
6.
FLASHCARD QUESTION
Front
What is the significance of multiplicity in polynomial roots?
Back
Multiplicity refers to the number of times a particular root appears in a polynomial. A root with an even multiplicity touches the x-axis, while a root with an odd multiplicity crosses the x-axis.
7.
FLASHCARD QUESTION
Front
What is the leading coefficient of a polynomial?
Back
The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in f(x) = 5x^4 + 2x^3 + 2x - 7, the leading coefficient is 5.
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