/*! 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 the given expressions com... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 11

Factor the given expressions completely. $$5 a-5$$

Short Answer

Expert verified
The expression is factored as \(5(a - 1)\).

Step by step solution

01

Identify the Common Factor

Start by observing the terms in the expression. The expression is \(5a - 5\). Both terms share a common factor, which is 5.
02

Factor Out the Greatest Common Factor

Factor out the greatest common factor (GCF) from the expression. In this case, factor 5 out of both terms: \[ 5(a - 1) \] This is the factored form of the expression.

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.

Common Factor
In algebra, a common factor is a value that divides each term of an expression without leaving a remainder. Recognizing common factors is crucial when simplifying expressions. For instance, in the expression \(5a - 5\), both terms have the number 5 as a common factor because 5 divides both 5 and itself neatly.

When we observe terms, looking for values or variables they share as common factors is the first step in simplifying them.
  • Identify numbers or variables that repeat in each term.
  • Check if there is a coefficient common to all terms.
By finding a common factor, you are laying the groundwork to simplify the expression further.
Greatest Common Factor
The greatest common factor (GCF) is the highest value that divides each term in an expression perfectly.

Factoring with the GCF can significantly simplify solving algebraic expressions and equations. For example, in the expression \(5a - 5\), the common factors of the terms are found, but 5 is the greatest that both 5 and 0 (since \(a\) represents any number) share. Therefore, we use 5 to simplify both terms simultaneously.

Here鈥檚 how you can determine the GCF:
  • List all factors of each term.
  • Identify the largest number common to all lists.
By factoring out the GCF, you streamline expressions, making them easier to manipulate or solve.
Expressions
An expression is a combination of numbers, variables, and operations (like addition or subtraction) that together form a mathematical phrase.

Expressions are the backbone of algebra, allowing representation and manipulation of real-world quantities with symbols. In expressions like \(5a - 5\), each part plays a role:
  • \(5a\) denotes 5 times a certain value \(a\).
  • The \(-5\) is a constant term that adjusts the expression's overall value.
Understanding each component's role within the expression helps comprehend the underlying mathematics.

Expressing complex problems with algebra helps us tackle them by using familiar operations and theorems.

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

Set up appropriate equations and solve the given stated problems. All numbers are accurate to at least two significant digits. A fox, pursued by a greyhound, has a start of 60 leaps. He makes 9 leaps while the greyhound makes but \(6 ;\) but, 3 leaps of the greyhound are equivalent to 7 of the fox. How many leaps must the greyhound make to overcome the fox? (Source: Elementary Algebra: Embracing the First Principles of the Science by Charles Davies, A.S. Barnes \& Company, 1852) (Hint: Let the unit of distance be one fox leap.)

Factor the expressions completely. In Exercises 73 and \(74,\) it is necessary to set up the proper expression. Each expression comes from the technical area indicated. \(4 d^{2} D^{2}-4 d^{3} D-d^{4} \quad\) (machine design)

Solve the given equations and check the results. $$\frac{2}{s}=\frac{3}{s-1}$$

Solve the given equations and check the results. $$\frac{6}{4 x-6}+\frac{2}{4}=\frac{6}{3-2 x}$$

Solve the given equations and check the results. $$\frac{1}{2 R}=\frac{2}{3 R}+\frac{1}{3}$$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Calculus

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.