Problem 500 Determine the degree of each pol... [FREE SOLUTION]

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Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 10: Problem 500

Determine the degree of each polynomial. $$-15$$

Short Answer

Expert verified

The degree is 0.

Step by step solution

Identify the Polynomial

The given expression is $-15$. This is a constant term, without any variable.

Understand the Degree of a Constant

The degree of a constant term is always 0 because there is no variable with an exponent. Constants are essentially $x^0$.

State the Degree

Therefore, the degree of the polynomial $-15$ is 0.

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Key Concepts

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

constant term

A constant term in a polynomial is a number that does not change. Unlike other terms in a polynomial, it has no variable attached to it. For example, in the expression \-15\, the term -15 is a constant term because there is no variable like $x$ or $y$ associated with it. This makes constant terms very easy to identify and work with.
Constant terms are unique because they represent a fixed quantity. They do not change regardless of what values variables in an equation might take.

polynomial

A polynomial is an algebraic expression that consists of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication. Essentially, a polynomial is a sum of several terms that can look something like this: $3x^2 + 4x - 5$.
Each term in a polynomial includes:

A coefficient (a number that multiplies the variable)
A variable (like x or y)
An exponent (a power to which a variable is raised)

The simplest polynomial is just a constant term, like \-15\ or \4\. More complex polynomials, such as $2x^3 + 5x - 7$, involve both variables and coefficients.

degree of a polynomial

The degree of a polynomial is the highest power of the variable in the expression. It tells us the most significant term in terms of growth and dominance as the variable increases. For instance, in the polynomial $4x^3 + 3x^2 - 2x + 1$, the degree is 3 since $x^3$ is the highest power.

When dealing with constant terms like $-15$, it might seem tricky to understand the degree since there's no variable. However, remember that any constant term can be seen as being multiplied by $x^0$ (since $x^0 = 1$). Therefore, the degree of any constant term is 0.

To sum up, degrees of a polynomial:

Identify the term with the highest exponent
Constant terms always have a degree of 0
The degree informs us about the general shape and behavior of the polynomial.

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91影视

Determine the degree of each polynomial. $$-15$$

Short Answer

Step by step solution

Identify the Polynomial

Understand the Degree of a Constant

State the Degree

Key Concepts

constant term

polynomial

degree of a polynomial

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