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Chapter 10: Problem 16

Identify the coefficient of each term. a. \(9 a b\) b. \(-4 y^{7}\) c. \(-8\) d. \(c d\)

Short Answer

Expert verified
a. 9, b. -4, c. -8, d. 1

Step by step solution

01

Understanding Coefficients

The coefficient is the numerical factor in a term. It is the number by which the variable(s) are multiplied.
02

Identify Coefficient in Term (a)

For the term \(9ab\), the numerical factor (coefficient) is 9.
03

Identify Coefficient in Term (b)

For the term \(-4y^{7}\), the numerical factor (coefficient) is -4.
04

Identify Coefficient in Term (c)

For the term \(-8\), there are no variables, so the term itself is the coefficient. The coefficient is -8.
05

Identify Coefficient in Term (d)

For the term \(cd\), there is no numerical factor explicitly stated. Thus, the coefficient is understood to be 1.

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Key Concepts

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

Numerical Factor
The numerical factor in a term is the number that multiplies the variable(s). It indicates the magnitude of the variable. For example, in the term\( 9ab \), the number 9 is the numerical factor. It tells us that the variables \( a \) and \( b \) are each multiplied by 9. When identifying the numerical factor, look for the standalone number that accompanies the variable.
Term
A term is a single mathematical expression that can be a number, a variable, or a combination of numbers and variables multiplied together. Each term in an expression is separated by addition or subtraction. For instance, in the expression \( 9ab + 2c - 5d \), there are three distinct terms: \( 9ab \), \( 2c \), and \( -5d \). Understanding terms helps in identifying the parts of an expression, making it easier to solve and simplify.
Variable
A variable represents an unknown value in a mathematical expression. It is usually denoted by a letter, such as \( a \), \( b \), or \( x \). Variables can change and represent different numbers at different times. In the term \( -4y^{7} \), \( y \) is the variable. It allows us to generalize mathematical relationships and solve equations for different possible values.
Coefficient
The coefficient is the numerical factor of a term. It shows how many times the variable is multiplied. For example, in the term \( -4y^{7} \), the coefficient is -4. If there's no numerical factor explicitly written with a variable, it is assumed to be 1, as seen in \( cd \), where the coefficient is 1. Knowing how to identify the coefficient is crucial for simplifying expressions and solving equations.

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Most popular questions from this chapter

Simplify. Write the answers with positive exponents only. $$8^{2} 8^{-4}$$

Which is greater? \(\left(2^{3}\right)^{2}\) or \(\left(2^{2}\right)^{3}\)

Simplify the expression. $$(3 t)^{2}$$

Simplify the expression. $$\left(\frac{9 a^{4}}{b}\right)^{2}$$

Simplify the expression. $$\left(\frac{z}{2}\right)^{3}$$
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