Problem 13 In the following exercises, dete... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 10: Problem 13

In the following exercises, determine the degree of each polynomial. $$-13$$

Short Answer

Expert verified

Step by step solution

Identify the polynomial

A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. Here, the given expression is $-13$, which can be considered as a polynomial.

Express in standard polynomial form

The standard form of a polynomial is given by \[a_n x^n + a_{n-1} x^{n-1} + \ldots + a_1 x + a_0\] In this case, $-13$ can be written as $-13x^0$.

Determine the degree

The degree of a polynomial is the highest power of the variable in the expression. In the expression $-13x^0$, the highest power of \x\ is 0.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Polynomial Expression

Let's start by understanding what a polynomial expression is. A polynomial is a mathematical expression that consists of variables, coefficients, and exponents. It is formed by adding several terms together. Each term must have a non-negative integer exponent. For example, expressions like $2x^3 + 3x^2 - 5$ or $7y^4 - y + 6$ are polynomials. These expressions include

Variables (e.g., x, y)
Coefficients (e.g., 2, 3, 7)
Exponents (non-negative integers)

In the given exercise, $-13$ is considered a polynomial expression even though it does not explicitly show a variable.

Standard Polynomial Form

Now, let's discuss the standard polynomial form. This form is a way to write the polynomial so that the terms are arranged from the highest degree to the lowest degree. A general polynomial in standard form looks like this: \[a_n x^n + a_{n-1} x^{n-1} + \cdots + a_1 x + a_0\] where

$a_n$ to $a_0$ are the coefficients
$x^n$ to $x^0$ are the terms with decreasing powers of the variable x.

In the exercise, we are given the number $-13$. To express this in standard form, we write it as $-13x^0$, where it is clear that the exponent on x is 0. This arrangement shows that even constants can be expressed as polynomials.

Degree of Polynomial

Finally, let's understand the degree of a polynomial. The degree of a polynomial is the highest power of the variable in the expression. It gives you an idea of the 'largest' term in the polynomial. For instance, in the polynomial $2x^3 + 3x^2 - 5$, the highest power of x is 3, so its degree is 3. In another example, $7y^4 - y + 6$, the term with the highest exponent is $7y^4$, which means the degree is 4. In our exercise, we have $-13x^0$. Here, the highest power of x is 0. Thus, the degree of this polynomial is 0. Even though $-13$ looks like a simple constant, it is fundamentally a polynomial of degree 0.

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91影视

In the following exercises, determine the degree of each polynomial. $$-13$$

Short Answer

Step by step solution

Identify the polynomial

Express in standard polynomial form

Determine the degree

Key Concepts

Polynomial Expression

Standard Polynomial Form

Degree of Polynomial

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