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Chapter 2: Problem 81

What is a polynomial inequality?

Short Answer

Expert verified
Polynomial Inequality is an inequality that involves a polynomial. It's a statement that an algebraic expression involving variables and operations such as addition, multiplication, and non-negative integer exponentiation of variables is greater than, less than, or equal to another polynomial. An example could be \(2x^2 - 3x + 1 > 0\). The goal when solving polynomial inequalities is to find the range of values that satisfy the inequality.

Step by step solution

01

Introduction to Polynomial

A polynomial is an expression consisting of variables and coefficients that involves the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. A typical form of a polynomial can be \(5x^3 + 4x^2 - 3x + 1\) where \(x\) is a variable, \(5, 4, -3, 1\) are coefficients, and \(3, 2, 1, 0\) are the powers.
02

Understanding Inequality

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value. A common type of this are numerical inequalities such as \(1 < 3\) or algebraic like \(x > 5\).
03

Definition of Polynomial Inequalities

A polynomial inequality is an inequality that involves a polynomial. For instance \(2x^2 - 3x + 1 > 0\). The main objective while solving such inequalities is to find the range of values of the variable for which the inequality stands true.

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Most popular questions from this chapter

Use transformations of \(f(x)=\frac{1}{x}\) or \(f(x)=\frac{1}{x^{2}}\) to graph each rational function. $$h(x)=\frac{1}{(x-3)^{2}}+1$$

a. Find the slant asymptote of the graph of each rational function and \(\mathbf{b} .\) Follow the seven-step strategy and use the slant asymptote to graph each rational function. $$f(x)=\frac{x^{2}-x+1}{x-1}$$

a. Find the slant asymptote of the graph of each rational function and \(\mathbf{b} .\) Follow the seven-step strategy and use the slant asymptote to graph each rational function. $$f(x)=\frac{x^{3}+1}{x^{2}+2 x}$$

a. Find the slant asymptote of the graph of each rational function and \(\mathbf{b} .\) Follow the seven-step strategy and use the slant asymptote to graph each rational function. $$f(x)=\frac{x^{2}-1}{x}$$

What is a rational inequality?
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