How do you determine the end behavior of the polynomial $$f(x) = x^3 + 2x^2 - 5x$$ ?

As $$x \to -\text{infinity}, f(x) \to -\text{infinity}$$ and as $$x \to +\text{infinity}, f(x) \to +\text{infinity}$$ .

What is a non-polynomial expression?

A non-polynomial expression includes variables raised to negative powers, fractional powers, or variables in the denominator. For example, $$\frac{1}{x} + 2x^2$$ is not a polynomial.

What is the difference between a monomial and a polynomial?

A monomial is a polynomial with only one term, such as $$3x^2$$ . A polynomial can have multiple terms, such as $$2x^3 + 3x^2 - 5x + 7$$ .

What is the significance of the leading term in a polynomial?

The leading term of a polynomial determines the end behavior of the polynomial function and influences the shape of its graph.

How do you identify the degree of a polynomial from its graph?

The degree of a polynomial can often be inferred from the number of turning points in its graph. A polynomial of degree n can have at most n-1 turning points.

What is a zero of a polynomial?

A zero of a polynomial is a value of x that makes the polynomial equal to zero. For example, if $$f(x) = x^2 - 4$$ , then the zeros are $$x = 2$$ and $$x = -2$$ .

What is the Fundamental Theorem of Algebra?

The Fundamental Theorem of Algebra states that every non-constant polynomial function has at least one complex root, and a polynomial of degree n has exactly n roots (counting multiplicities).

What is the difference between even and odd degree polynomials?

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

How do you convert a polynomial to standard form?

To convert a polynomial to standard form, rearrange the terms in descending order based on the degree of each term.

Flashcard 1 Review - Polynomials Intro Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a polynomial?

Back

2.

FLASHCARD QUESTION

Front

What is the standard form of a polynomial?

Back

3.

FLASHCARD QUESTION

Front

What is the degree of a polynomial?

Back

4.

FLASHCARD QUESTION

Front

What is the leading coefficient of a polynomial?

Back

5.

FLASHCARD QUESTION

Front

What does it mean for a polynomial to be in standard form?

Back

A polynomial is in standard form when its terms are written in descending order of their degrees, with the highest degree term first.

6.

FLASHCARD QUESTION

Front

What is the end behavior of a polynomial function?

Back

The end behavior of a polynomial function describes how the function behaves as the input values approach positive or negative infinity. It is determined by the degree and leading coefficient.

7.

FLASHCARD QUESTION

Front

Back

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