Problem 91 - College Algebra

Question

What is a polynomial in \(x ?\)

Step-by-Step Solution

Answer

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 1: 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.

Step 2: 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.