/*! 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 33 Factor out the GCF. $$ 25 x-... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 33

Factor out the GCF. $$ 25 x-16 $$

Short Answer

Expert verified
The expression cannot be factored further; it's already in simplest form.

Step by step solution

01

Identify the Terms

The given expression is \(25x - 16\). It consists of two terms: \(25x\) and \(-16\).
02

Determine the GCF

To find the GCF (Greatest Common Factor), look at the coefficients of the terms and any common variables. For \(25x\), the coefficient is 25, and there is a variable \(x\). For \(-16\), the coefficient is 16. The greatest common factor of 25 and 16 is 1, as they share no other common divisors, and there is no variable common between the terms.
03

Factor Out the GCF

Since the GCF is 1, we can express the factorization as: \(1(25x - 16)\). However, factoring by 1 doesn't change the expression, so it remains \(25x - 16\).

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.

Factoring
Factoring is like breaking down numbers or expressions into simpler parts. It鈥檚 like finding the ingredients of a cake to understand what it鈥檚 made of. When you factor, you are looking for elements that multiply together to form the whole.
  • Basic Concept: Factoring involves expressing a number or expression as a product of its factors. For example, the number 12 can be factored into 2, 2, and 3, since \(2 \times 2 \times 3 = 12\).
  • In Algebra: Factoring an algebraic expression means finding numbers or expressions that multiply to form the original expression. When factoring \(25x - 16\), we鈥檙e looking to see if there鈥檚 a common number or variable we can take out of both terms.
Factoring is an essential skill in algebra because it simplifies expressions and helps solve equations.
Algebraic Expressions
Algebraic expressions are like mathematical sentences that use numbers, variables, and operations. They can express quantities and relationships in algebra.
  • Structure: An algebraic expression consists of terms that are either separated by plus or minus signs. For instance, in the expression \(25x - 16\), \(25x\) and \(-16\) are the terms.
  • Components: Each term is made up of numbers called coefficients, and may include variables (like \(x\) in \(25x\)).
  • Simplifying: Simplifying an expression is about finding the most straightforward form, often by combining like terms or factoring.
Understanding algebraic expressions is crucial because they are the foundation of algebraic equations and problem-solving.
Coefficients
Coefficients are the numbers in front of the variables in a term of an algebraic expression. They are important because they indicate how many times a variable is multiplied.
  • Identify: In the term \(25x\), 25 is the coefficient. It tells us that \(x\) is considered 25 times in that term.
  • Role in Factoring: When finding the GCF, coefficients are examined to see if they have any common factors. This is key when simplifying expressions.
  • Relationship with Variables: A term doesn't have to include a variable, such as the term \(-16\), which is a standalone coefficient.
By understanding coefficients, you can break down expressions accurately and solve algebraic problems efficiently.

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

The height of a triangle is 4 units less than the length of the base. If the area of the triangle is 48 square units, then find the length of its base and height.

A uniform border is to be placed around an 8 -inch-by-10-inch picture. If the total area including the border must be 224 square inches, then how wide should the border be?

The height of a projectile, shot straight up into the air from the ground at 128 feet/second, is given by \(h(t)=-16 t 2+128 t .\) How long does it take to come back down to the ground?

Factor completely. $$ 15 a_{2} b_{2}-57 a b-12 $$

The height of a projectile launched upward at a speed of 32 feet/second from a height of 48 feet is given by the function \(h(t)=-16 t 2+32 t+48 .\) How long will it take the projectile to hit the ground?
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Statistics

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.