Problem 151 In the following exercises, iden... [FREE SOLUTION]

Chapter 1: Problem 151

In the following exercises, identify the terms in each expression. $$ 10 y^{3}+y+2 $$

Short Answer

Expert verified

The terms are $10y^{3}$, $y$, and $2$.

Step by step solution

- Identify the First Term

The first term is the part of the expression that includes the highest power of the variable. In this expression, it is the term with the variable raised to the power of three, which is $10y^{3}$.

- Identify the Second Term

The second term is the part of the expression with the variable raised to the power of one. In this expression, it is the term $y$.

- Identify the Constant Term

The third term is the constant term. This term does not have any variables. In this expression, it is $2$.

Summary of Terms

The three terms are $10y^{3}$, $y$, and $2$.

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Key Concepts

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

Identifying Terms in Expressions

When you look at a mathematical expression, it is made up of parts called terms. Each term is a piece of the expression that can be a number, a variable (like x or y), or a variable raised to a power (like y^3).

In the expression given, we have three terms: 10y^3, y, and 2. Breaking it down like this makes it easier to understand and solve algebra problems.
Understanding how to identify terms in an expression is a key skill in algebra. It helps you manage and manipulate expressions, making complex problems more manageable.

Polynomial Terms

Polynomials are mathematical expressions that consist of variables raised to whole number powers and coefficients. The terms we identify within these polynomials can have different powers.

In our example, the term 10y^3 represents a polynomial term. Here are some details to help understand:

10: This is the coefficient of y^3.
y^3: This signifies that y is raised to the power of 3.

Polynomials can have several terms with variables raised to different powers. Knowing how to distinguish between these terms helps in solving and simplifying polynomial expressions.

Constant Term

In any algebraic expression, a constant term is a number that stands alone without a variable. It鈥檚 essential to identify it since it doesn't change regardless of the value of other variables.

Our example has the constant term 2. This constant term sits by itself and does not include any variables, making it straightforward to spot.

Constant: A numeral that remains unchanged.

Recognizing the constant term helps you better understand the structure of an algebraic expression and how different parts of the expression interact.

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91影视

In the following exercises, identify the terms in each expression. $$ 10 y^{3}+y+2 $$

Short Answer

Step by step solution

- Identify the First Term

- Identify the Second Term

- Identify the Constant Term

Summary of Terms

Key Concepts

Identifying Terms in Expressions

Polynomial Terms

Constant Term

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