What is the factored form of the polynomial $$f(x) = 3x^4 - 12x^2$$ ?

The factored form is $$f(x) = 3x^2(x + 2)(x - 2)$$ .

What is the end behavior of the polynomial $$f(x) = 3x^4 - 12x^2$$ ?

As $$x \rightarrow \infty, f(x) \rightarrow \infty$$ and as $$x \rightarrow -\infty, f(x) \rightarrow \infty$$ .

What does it mean for a zero to have multiplicity?

The multiplicity of a zero refers to the number of times that zero is repeated as a root of the polynomial.

How do you find the zeros of a polynomial?

To find the zeros of a polynomial, set the polynomial equal to zero and solve for the variable.

What is a rational function?

A rational function is a function that can be expressed as the ratio of two polynomials, i.e., $$f(x) = \frac{p(x)}{q(x)}$$ , where $$p(x)$$ and $$q(x)$$ are polynomials.

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

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

What is the difference between a maximum and a minimum in a graph?

A maximum is the highest point on a graph within a given interval, while a minimum is the lowest point.

What is the purpose of factoring a polynomial?

Factoring a polynomial helps to find its zeros and simplifies the process of solving polynomial equations.

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 a polynomial with an even degree and a positive leading coefficient?

The end behavior will be such that as $$x \rightarrow \infty, f(x) \rightarrow \infty$$ and as $$x \rightarrow -\infty, f(x) \rightarrow \infty$$ .

2 Review Polynomials and Rational Functions

Flashcard

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Mathematics

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9th - 12th Grade

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Practice Problem

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Hard

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CCSS

HSF-IF.C.7C, HSF-BF.A.1C, HSF-IF.C.7D

Standards-aligned

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FLASHCARD QUESTION

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The zeros are 0 with multiplicity 2, -2 with multiplicity 1, and 2 with multiplicity 1.

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