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Chapter 0: Problem 91

What is a polynomial in \(x ?\)

Short Answer

Expert verified
A polynomial in \(x\) is an algebraic expression of the form \(a_nx^n + a_{n-1}x^{n-1} + \ldots + a_2x^2 + a_1x + a_0\), where \(a_i\) is a real number (coefficient), n is a non-negative integer (degree of the polynomial), \(x\) is the variable, and the exponents of the variable \(x\) are non-negative integers.

Step by step solution

01

Definition of Polynomial

In terms of algebra, a polynomial is an expression consisting of variables and coefficients. Usually the variables or sometimes called the indeterminates are denoted by one letter such as \(x\), \(y\) or \(z\). The exponents of the variables are non-negative integers and coefficients are any real numbers, often represented by \(a\), \(b\), \(c\), and so on.
02

Polynomial in \(x\)

A Polynomial in the variable \(x\) is of the form: \(a_nx^n + a_{n-1}x^{n-1} + \ldots + a_2x^2 + a_1x + a_0\), where each \(a_i\) is a real number and is called the coefficient of \(x^i\), and n is a non-negative integer and is called the degree of the polynomial. The term with the highest degree is called the leading term, and its coefficient is called the leading coefficient.

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Most popular questions from this chapter

Simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. $$ \frac{4 x-8}{x^{2}-4 x+4} $$

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evaluate each algebraic expression for the given value of the variable or variables. $$ \frac{2 x+3 y}{x+1} ; x=-2 \text { and } y=4 $$

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In Exercises \(1-10\), factor out the greatest common factor. $$x^{2}(2 x+5)+17(2 x+5)$$
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