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

A polynomial of degree $$n$$ can have up to $$n$$ real zeros, counting multiplicities. This means that a polynomial of degree 3 can have 1, 2, or 3 real zeros.

What is a multiplicity of a zero?

The multiplicity of a zero refers to the number of times a particular zero appears as a root of the polynomial. For example, if $$(x - 2)^2$$ is a factor, then 2 is a zero with multiplicity 2.

What is the end behavior of a polynomial function?

The end behavior of a polynomial function describes how the function behaves as $$x$$ approaches positive or negative infinity. It is determined by the leading term.

What is the difference between even and odd degree polynomials?

Even degree polynomials have the same end behavior on both sides (both up or both down), while odd degree polynomials have opposite end behavior (one side up, the other down).

How can you identify the graph of a polynomial function?

You can identify the graph of a polynomial function by looking for its x-intercepts, y-intercept, and the general shape based on the degree and leading coefficient.

What is the y-intercept of a polynomial function?

The y-intercept of a polynomial function is the point where the graph intersects the y-axis. It can be found by evaluating the polynomial at $$x = 0$$ .

What is the role of the leading term in determining the shape of a polynomial graph?

The leading term determines the end behavior of the polynomial graph. It influences whether the graph rises or falls as $$x$$ approaches positive or negative infinity.

What is a polynomial equation?

A polynomial equation is an equation that sets a polynomial expression equal to a value, typically zero. For example, $$f(x) = 0$$ is a polynomial equation.

CH4 test 2nd 9 wks. 2024-25 Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a polynomial function?

Back

2.

FLASHCARD QUESTION

Front

What does it mean for a number to be a zero of a polynomial?

Back

3.

FLASHCARD QUESTION

Front

How do you determine if a number is a zero of a polynomial?

Back

4.

FLASHCARD QUESTION

Front

What is the degree of a polynomial?

Back

5.

FLASHCARD QUESTION

Front

What is the leading coefficient of a polynomial?

Back

6.

FLASHCARD QUESTION

Front

What is the factored form of a polynomial?

Back

7.

FLASHCARD QUESTION

Front

What is the significance of the x-intercepts of a polynomial function?

Back

The x-intercepts of a polynomial function are the points where the graph intersects the x-axis. These points correspond to the zeros of the polynomial.

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