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Chapter 5: Problem 107

What is a polynomial?

Short Answer

Expert verified
A polynomial is an algebraic expression made up of terms, where each term is a constant times a variable raised to a non-negative integer exponent. For example, \(4x^3 + 2x^2 - 3x + 1 \) is a polynomial.

Step by step solution

01

Definition of Polynomial

A polynomial is an expression consisting of variables and coefficients, arranged in terms of increasing power of the variable. It employs the operations of addition, subtraction, multiplication and non-negative whole number exponents of variables. Note that division by a variable is not permitted.
02

Structure of Polynomial

Polynomials are of the form \( a_n x^n + a_{n-1} x^{n-1} + . . . + a_2 x^2 + a_1 x + a_0 \) where each of 'x' are variables, 'n' is a non-negative integer and each of 'a' are coefficients. The highest power of 'x' is known as the degree of the polynomial.
03

Example of Polynomial

An example of a polynomial is \(4x^3 + 2x^2 - 3x + 1 \). In this polynomial, 'x' is the variable, 4, 2, -3, 1 are the coefficients and 3 is the degree of the polynomial.

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Most popular questions from this chapter

Use a vertical format to find each product. $$\begin{array}{l}x^{2}+7 x-3 \\\x^{2}-x-1 \\\\\hline\end{array}$$

In Exercises \(79-82,\) simplify each expression. $$\frac{2 x^{3}(4 x+2)-3 x^{2}(2 x-4)}{2 x^{2}}$$

In each exercise, find the product. $$(x+3)\left(x^{2}+5\right)$$

Exercises \(110-112\) will help you prepare for the material covered in the next section. In each exercise, perform the long division without using a calculator, and then state the quotient and the remainder. $$. 9 8 \longdiv { 2 5 . 1 8 7 }$$

Will help you prepare for the material covered in the next section. In each exercise, find the indicated products. Then, if possible, state a fast method for finding these products. (You may already be familiar with some of these methods from a high school algebra course.) a. \((x+3)(x-3)\) b. \((x+5)(x-5)\)
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