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

The number of zeros of a polynomial is related to its degree. A polynomial of degree n can have up to n real zeros, counting multiplicities.

What is a polynomial function?

A polynomial function is a function that can be represented by a polynomial equation. For example, $$f(x) = 2x^2 + 3x - 5$$ is a polynomial function.

What is the standard form of a polynomial?

The standard form of a polynomial is written in descending order of the degree of its terms. For example, $$f(x) = 4x^3 + 2x^2 - x + 7$$ is in standard form.

What is the significance of the zeros of a polynomial in graphing?

The zeros of a polynomial indicate where the graph intersects the x-axis. They are critical points for determining the shape of the graph.

What is synthetic division?

Synthetic division is a simplified method of dividing a polynomial by a linear factor of the form $$(x - c)$$ . It is faster than long division for polynomials.

What is the Remainder Theorem?

The Remainder Theorem states that if a polynomial $$f(x)$$ is divided by $$(x - c)$$ , the remainder is $$f(c)$$ .

What is the Factor Theorem?

The Factor Theorem states that a polynomial $$f(x)$$ has a factor $$(x - c)$$ if and only if $$f(c) = 0$$ .

What is the end behavior of a polynomial?

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

Graphs of Polynomials 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 are the zeros of a polynomial?

Back

3.

FLASHCARD QUESTION

Front

How do you find the zeros 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

How many zeros can a polynomial have?

Back

A polynomial of degree n can have at most n zeros. For example, a quadratic polynomial (degree 2) can have up to 2 zeros.

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