Problem 56 Write in factored form by factor... [FREE SOLUTION]

91影视

Beginning Algebra

Margaret L. Lial, John Hornsby

$Math Studyset 91影视 Explanations$ Math

11 Edition

Chapter 6: Problem 56

Write in factored form by factoring out the greatest common factor. $r(x+5)-t(x+5)$

Short Answer

Expert verified

(x+5)(r-t)

Step by step solution

Identify the common factor

Look for a common term in each part of the expression. In this case, the common term is $x+5$.

Factor out the common term

Take $x+5$ outside of the parentheses, which leaves $r-t$ inside the parentheses.

Write the final factored form

Combine the common factor and the remaining terms: \[ (x+5)(r-t) \]. This is the factored form of the given expression.

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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 a key concept in algebra, and it's the largest number or expression that divides exactly into each term of the expression. When we talk about algebraic expressions, we're not just looking at numbers. We also need to account for whole terms consisting of variables, numbers, and coefficients. Finding the GCF involves:
- Identifying common factors in each term.
- Using these common factors to simplify the expression.
In our example, the shared factor is $x + 5$. This term appears in both parts of the expression $r(x+5) - t(x+5)$. Hence, it鈥檚 the greatest common factor we can factor out of this expression.

Factored Form

Factored form is another important concept. It refers to expressing an algebraic expression as a product of its factors. Essentially, it's about breaking down the expression into simpler parts. For example, if we start with $r(x + 5) - t(x + 5)$, factored form means taking out the greatest common factor $GCF$. This process involves:
- Identifying common terms.
- Grouping these common terms together.
After factoring out $x + 5$ from the original expression, we get $(x + 5)(r - t)$. Here, $x + 5$ is the GCF, and $(r - t)$ is what remains inside the parentheses. Putting these together gives us the factored form.

Algebraic Expressions

Algebraic Expressions consist of variables, numbers, and operators (like +, -, *, /). They represent mathematical phrases that can be simplified or manipulated. When dealing with these expressions, it's crucial to understand how to:
- Simplify them.
- Factorize them.
In our example, the initial expression is $r(x + 5) - t(x + 5)$. By recognizing that $x + 5$ is present in both terms, we can simplify the expression to its factored form $(x + 5)(r - t)$. This simplification makes it easier to solve equations or further manipulate the expression in algebraic operations.

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91影视

Write in factored form by factoring out the greatest common factor. \(r(x+5)-t(x+5)\)

Short Answer

Step by step solution

Identify the common factor

Factor out the common term

Write the final factored form

Key Concepts

Greatest Common Factor

Factored Form

Algebraic Expressions

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