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Chapter 2: Problem 58

Factor the given expression by taking out the common factor. $$3 x+12$$

Short Answer

Expert verified
3(x + 4)

Step by step solution

01

Identify the Common Factor

Examine the terms in the expression. Both terms in the expression are multiples of 3.
02

Factor Out the Common Factor

Factor 3 out from each term in the expression. This simplifies the expression. The expression becomes: 3(x + 4)

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Key Concepts

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

Common Factor
Understanding the common factor is the first step in simplifying algebraic expressions. A common factor is a number or variable that divides each term in the expression without leaving a remainder.
When identifying a common factor, ask yourself:
  • Can I divide all terms by the same number?
  • Do the terms share a variable with the same or lower exponent?

In our example of the expression \(3x + 12\), both terms (\(3x\) and \(12\)) are multiples of 3. Here, 3 is the common factor.
Recognizing common factors makes it easier to break down complex algebraic expressions into simpler forms.
Algebraic Expressions
Algebraic expressions consist of terms, which may contain numbers, variables, and exponents. Terms are parts of the expression separated by plus or minus signs. For instance, in our example expression \(3x + 12\):
  • \(3x\) is one term
  • \(12\) is another term

These terms are connected by the '+' sign. Understanding the structure of these expressions is essential for effective manipulation, simplification, and factoring.
Simplifying Expressions
Simplifying expressions involves reducing them to their simplest form. This process often entails factoring out common factors, combining like terms, or performing arithmetic.
In the given exercise, we simplify \(3x + 12\) by factoring out the common factor (3):
  • Start by dividing each term by 3
  • You get \(3(x + 4)\)

This is the simplified form of the original expression. By taking out the common factor, we make the expression easier to work with and understand.

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Most popular questions from this chapter

Simplify by combining like terms whenever possible. $$5 x\left(x^{2}+3\right)+2 x\left(3 x^{2}\right)$$

Evaluate the given expression for \(x=0.24\) and \(y=-0.5 .\) Round off to the nearest thousandth where necessary. $$10 x^{3}+20 y$$

Simplify by combining like terms whenever possible. $$-3 x^{2}+5 x y-x y-x^{2}-2 x^{2}$$

Simplify by combining like terms whenever possible. $$0.085 x+28.75+0.072 x+54.8$$

Simplify by combining like terms whenever possible. $$y^{2}-6 y+y^{2}-y$$
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