/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 11 Factor each expression. $$3 n+... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 11

Factor each expression. $$3 n+9$$

Short Answer

Expert verified
The factored expression is \(3(n + 3)\).

Step by step solution

01

Identify the Common Factor

The first step in factoring any expression is to identify the greatest common factor (GCF) of the terms. In the expression \(3n + 9\), observe the coefficients and terms: \(3n\) and \(9\). Both terms are divisible by \(3\). Thus, the GCF is \(3\).
02

Apply the Distributive Property

Use the distributive property to factor out the GCF. Divide each term by the GCF and rewrite the expression. \[3n + 9 = 3(n + 3)\] Here, we factor out \(3\) from the expression, leaving us with \(n + 3\) inside the parenthesis.
03

Check Your Work

Finally, it is crucial to check if the factoring is done correctly by expanding the factored expression. Use distribution: \[3(n + 3) = 3n + 9\] This matches the original expression, confirming the factoring is correct.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Greatest Common Factor
The greatest common factor (GCF) is the largest number that divides each term in an expression without leaving a remainder. When we look at the expression \(3n + 9\), both terms, \(3n\) and \(9\), need to be considered.
  • For the term \(3n\): The coefficient is \(3\).
  • For the term \(9\): The number itself is \(9\).
  • Both \(3\) and \(9\) are divisible by \(3\).
Thus, the GCF of \(3n\) and \(9\) is \(3\). Factoring makes expressions simpler by showing the building blocks of the terms, which is especially helpful in solving algebraic equations.
Distributive Property
The distributive property allows us to break down expressions into simpler parts by taking a common factor and distributing it across terms.When we apply it to the expression \(3n + 9\):
  • We factor out the GCF, which is \(3\).
  • Express the original terms as products of the GCF.
So, \(3n + 9\) can be written as \(3(n + 3)\). Hence, \(3\) is distributed across \(n + 3\), simplifying the expression and making it easier to work with in more complex equations.
Algebraic Expressions
Algebraic expressions are combinations of variables, numbers, and operations such as addition and multiplication. They are the building blocks of algebra and essential in expressing real-life problems mathematically.In the expression \(3n + 9\):
  • \(3n\): This is a term with a coefficient \(3\) and a variable \(n\).
  • \(+ 9\): A constant term added to \(3n\).
When factoring, we see that these expressions can be decomposed into simpler terms using the concepts of the greatest common factor and the distributive property to enhance understanding and solve for unknown variables efficiently. Factoring helps in transforming complex expressions, which forms the cornerstone of many algebraic processes.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Find each product or quotient. Express using exponents. $$\frac{36 d^{6}}{12 d^{4}}$$

Write each fraction in simplest form. If the fraction is already in simplest form, write simplified. $$\frac{17}{51}$$

Ninety-six centimeters is what part of a meter? $$\mathbf{A} \frac{3}{5}$$ $$B \frac{4}{5}$$ $$\text { C } \frac{23}{25}$$ $$\mathbf{D} \frac{24}{25}$$

Find each product. $$4.05 \times 10$$

Simplify each fraction. If the fraction is already in simplest form, write simplified. \(\frac{4 k}{19 m}\)
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.