Problem 3 Give the numerical coefficient a... [FREE SOLUTION]

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Chapter 5: Problem 3

Give the numerical coefficient and the degree of each term. $$ -15 p^{2} $$

Short Answer

Expert verified

Numerical coefficient: -15, Degree: 2.

Step by step solution

Identify the Term

The term given is $-15 p^{2}$. Break down its components.

Determine the Numerical Coefficient

The numerical coefficient is the constant part of the term. Here, it is $-15$.

Determine the Degree of the Term

The degree of the term is the exponent of the variable. In $-15 p^{2}$, the exponent is $2$.

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Key Concepts

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

Understanding the Degree of a Term

The degree of a term is an important concept in algebra. It refers to the power of the variable in the term. For example, in the term $-15 p^{2}$, the variable $p$ is raised to the power of $2$. Thus, the degree of the term is $2$. The degree tells us how many times the variable is multiplied by itself. It helps establish the term鈥檚 behavior in equations and its effect on graph shapes.You can often spot the degree of a term immediately by looking at the exponent of the variable.

Examining Polynomial Exponents

Polynomial exponents are the numbers to which the variables in a polynomial are raised. They play a crucial role in defining the shape and behavior of polynomial graphs. In the term $-15 p^{2}$, the exponent is $2$. Here鈥檚 a quick guide to understanding polynomial exponents:

Exponents indicate how many times to use the variable in multiplication.
Positive exponents mean the variable is multiplied by itself that many times.
Negative exponents indicate the reciprocal of the base raised to the absolute value of the exponent.
Exponents of $0$ mean the term equals $1$ (as long as the base is not zero).

Keep these points in mind when working with polynomial terms.

Recognizing Algebraic Terms

Algebraic terms are the building blocks of algebraic expressions. An algebraic term consists of a numerical coefficient, a variable, and an exponent. Let鈥檚 break down the term $-15 p^{2}$:

$ -15 $ is the numerical coefficient.
$ p $ is the variable.
$ 2 $ is the exponent.

Each part serves a unique purpose. The numerical coefficient tells us the quantity. The variable represents an unknown quantity. The exponent indicates how many times the variable multiplies by itself. Together, these parts form algebraic terms, which can then be combined to form algebraic expressions and equations. Understanding each element helps simplify and solve algebra problems more effectively.

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91影视

Give the numerical coefficient and the degree of each term. $$ -15 p^{2} $$

Short Answer

Step by step solution

Identify the Term

Determine the Numerical Coefficient

Determine the Degree of the Term

Key Concepts

Understanding the Degree of a Term

Examining Polynomial Exponents

Recognizing Algebraic Terms

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