What is the end behavior of a polynomial?

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

What is a polynomial function?

A polynomial function is a function that can be represented by a polynomial equation. For example, $$f(x) = 2x^3 - 4x + 1$$ is a polynomial function.

What is the difference between a monomial, binomial, and trinomial?

A monomial has one term (e.g., $$3x$$ ), a binomial has two terms (e.g., $$x + 2$$ ), and a trinomial has three terms (e.g., $$x^2 + 3x + 4$$ ).

How do you add polynomials?

To add polynomials, combine like terms. For example, $$(2x^2 + 3x) + (4x^2 + 5) = 6x^2 + 3x + 5$$ .

How do you multiply polynomials?

To multiply polynomials, use the distributive property (FOIL for binomials). For example, $$(x + 2)(x + 3) = x^2 + 5x + 6$$ .

What is synthetic division?

Synthetic division is a simplified method of dividing a polynomial by a linear divisor. It is faster than long division and is used when the divisor is of the form $$x - c$$ .

What is the Remainder Theorem?

The Remainder Theorem states that the remainder of the division of a polynomial $$f(x)$$ by $$x - c$$ is equal to $$f(c)$$ .

What is the Factor Theorem?

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

Key Features 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 is the degree of a polynomial?

Back

3.

FLASHCARD QUESTION

Front

What is a zero of a polynomial?

Back

4.

FLASHCARD QUESTION

Front

How do you find the zeros of a polynomial?

Back

5.

FLASHCARD QUESTION

Front

What is the factored form of a polynomial?

Back

6.

FLASHCARD QUESTION

Front

What is the leading coefficient of a polynomial?

Back

7.

FLASHCARD QUESTION

Front

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

Back

The maximum number of extrema (local maxima and minima) of a polynomial is one less than its degree. For example, a polynomial of degree 4 can have up to 3 extrema.

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