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

A polynomial of degree $$n$$ can have at most $$n$$ real zeros.

What is the end behavior of the polynomial $$f(x) = 3x^3 + 2x^2$$ ?

As $$x \rightarrow -\infty$$ , $$y \rightarrow -\infty$$ and as $$x \rightarrow +\infty$$ , $$y \rightarrow +\infty$$ .

What is the end behavior of the polynomial $$w(x) = x^2(x + 12)^2(x - 3)$$ ?

As $$x \rightarrow -\infty$$ , $$y \rightarrow -\infty$$ and as $$x \rightarrow +\infty$$ , $$y \rightarrow +\infty$$ .

What are the zeros of the polynomial $$p(x) = x^3(x - 8)^2(x + 1)^2$$ ?

The zeros are $$x = 0$$ , $$x = 8$$ , and $$x = -1$$ .

What is the end behavior of the polynomial $$m(x) = (x - 10)^2(x + 2)^2$$ ?

As $$x \rightarrow -\infty$$ , $$y \rightarrow +\infty$$ and as $$x \rightarrow +\infty$$ , $$y \rightarrow +\infty$$ .

What is the end behavior of the polynomial $$m(x) = -x(x + 7)$$ ?

As $$x \rightarrow -\infty$$ , $$y \rightarrow +\infty$$ and as $$x \rightarrow +\infty$$ , $$y \rightarrow -\infty$$ .

What is the leading coefficient test?

The leading coefficient test helps determine the end behavior of a polynomial function based on the sign and degree of the leading term.

What is the difference between a polynomial function and a rational function?

A polynomial function is a function that can be expressed in the form $$f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0$$ , while a rational function is a ratio of two polynomial functions.

Polynomial End Behavior and zeros Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the end behavior of a polynomial function with an odd degree and a positive leading coefficient?

Back

2.

FLASHCARD QUESTION

Front

What is the end behavior of a polynomial function with an even degree and a positive leading coefficient?

Back

3.

FLASHCARD QUESTION

Front

What is the end behavior of a polynomial function with an odd degree and a negative leading coefficient?

Back

4.

FLASHCARD QUESTION

Front

What is the end behavior of a polynomial function with an even degree and a negative leading coefficient?

Back

5.

FLASHCARD QUESTION

Front

Define a zero of a polynomial function.

Back

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