Problem 11 In the following exercises, dete... [FREE SOLUTION]

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Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 10: Problem 11

In the following exercises, determine the degree of each polynomial. $$3 x-12$$

Short Answer

Expert verified

The degree of the polynomial is 1.

Step by step solution

Identify the terms

Identify each term in the polynomial. In this polynomial, the terms are 3x and -12.

Determine the exponents

Next, look at the exponents of the variable x in each term. In the term 3x, the exponent of x is 1. In the term -12, there is no variable x present, so its exponent is considered to be 0.

Identify the highest exponent

The degree of the polynomial is the highest exponent of the variable x in any of the terms. In this case, the highest exponent is 1, from the term 3x.

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Key Concepts

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

identifying terms in polynomials

Polynomials are algebraic expressions that consist of terms.
Each term is usually separated by a plus (+) or minus (鈭�) sign.
For example, in the polynomial $3x - 12$, the terms are '3x' and '-12'.
It's important to know that each term can have a coefficient (a number) and a variable (like x).
In '3x', '3' is the coefficient, and 'x' is the variable.
Sometimes, terms might not have a variable, like '-12'.
When identifying terms, remember that each term stands alone as a separate part of the polynomial.

determining exponents

An exponent tells you how many times to multiply the base (which is the variable).
When you see a term like '3x', there is an implicit exponent of 1 on the variable x.
This means it is the same as '3x^1'.
If a term like '-12' has no variable, the exponent is 0 because any number raised to the power of 0 is 1.
So, '-12' can be thought of as '-12x^0'.
Knowing how to identify the exponent in each term helps you understand the polynomial better and is crucial for finding the polynomial's degree.

highest exponent in polynomials

The highest exponent in a polynomial is called its degree.
The degree tells you the highest power to which any variable in the polynomial is raised.
For example, in the polynomial '3x - 12', the exponents are 1 and 0.
The highest of these exponents is 1.
So, the degree of the polynomial '3x - 12' is 1.
Finding the highest exponent helps you understand the polynomial's complexity and behavior.
It's a key part of solving and analyzing polynomials.

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91影视

In the following exercises, determine the degree of each polynomial. $$3 x-12$$

Short Answer

Step by step solution

Identify the terms

Determine the exponents

Identify the highest exponent

Key Concepts

identifying terms in polynomials

determining exponents

highest exponent in polynomials

One App. One Place for Learning.

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