Factoring is an essential part of algebra that helps us simplify complex expressions. It involves breaking down an expression into simpler terms or factors that are easy to work with.
One commonly used method of factoring is factoring out a number from an expression. Factoring out a number from an expression can help simplify an expression, making it easier to solve or simplify. Understanding how to factor out a number from an expression is a crucial skill for students dealing with algebraic equations, trigonometric functions, or calculus problems.
Keep reading to explore the rules and techniques of how to factor out a number from an expression. You might also enjoy reading: Differences Between PEMDAS, BODMAS, and BIDMAS.
Step 1: Identify The Common Factor
The first and most crucial step in factoring out a number from an expression is identifying the common factor, which is always a number that divides all the terms in the expression.
For instance, consider an expression like
- 6x + 12.
The common factor in this expression is 6 since this number divides evenly into both terms.
Step 2: Divide Each Term by The Common Factor
Once you have identified the common factor, you can now simplify the expression by dividing each term by the common factor.
For example, 6x +12 can be simplified by dividing the terms by the common factor 6, which will give the expression x + 2. Now, we have successfully factored out the number 6.
The equation then becomes 6(x + 2)
Step 3: Check Your Answer
Always check your answer after you’ve factored out a number from an expression, as it will help to ensure that you haven’t made any errors while simplifying the expression.
Step 4: Apply to More Complex Expressions
For instance, consider an expression like 24xy + 36x2y. The common factor in this expression is 12xy since it divides evenly into both terms. Dividing each term by 12xy will give us the simplified expression 2y + 3x.
Step 5: Practice, Practice, Practice
Practice makes perfect. The more you practice factoring out numbers from expressions, the better you will get at it.
I encourage you to try to solve different problems from your textbooks or online resources. The more you practice, the more confident you become in your ability to factor out numbers from expressions.
Essential Tips To Remember When Factoring out a Number from an Expression:
When factoring out a number from an expression, we need to follow some essential rules.
- Ensure that the number we want to factor out is a factor of every term in the expression.
- Divide each term in the expression by that number.
- Place the number outside the parentheses and the remaining expression inside the parentheses.
Examples On How to Factor Out a Number From An Expression
Consider the expression 20x + 16y. We want to factor out the number 4.
- Check if 4 is a factor of both terms. 20 divided by 4 is 5, and 16 divided by 4 is 4. Hence, 4 is a factor of both terms.
- Divide each term in the expression by 4 as follows: 20x/4 + 16y/4, which simplifies to 5x + 4y.
- Write 4 outside the parentheses and 5x + 4y inside. Therefore, 20x + 16y can be factored as 4(5x + 4y).
- It is essential to note that we can also factor out negative numbers as well. For instance, consider the expression -18x – 12y. Therefore, -18x – 12y can be factored as -6(3x + 2y).
If you want to learn more about how to factor out a number from an expression, watch this video or the video below.
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Wrapping Up
Factoring out a number from an expression is an essential skill in algebra, trigonometry, and calculus. The steps involved in factoring are identifying the common factor, dividing each term by the common factor, and double-checking your answer.
Remember to follow the rules and techniques mentioned in this blog post when factoring out numbers from an expression.