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How do I Factor Out the Coefficient of the Variable?
In algebra, factoring is a technique used to simplify mathematical expressions by expressing them as a product of smaller factors. One common problem in algebra is factoring out the coefficient of the variable. This involves determining the greatest common factor (GCF) of the coefficients of the variable terms and then multiplying it by the variable.
For example, the expression 6x + 12 can be factored out by finding the GCF of 6 and 12, which is 6. We can then multiply the GCF by the variable x, resulting in the factored expression 6(x + 2).
Understanding the Concept
To factor out the coefficient of a variable, we need to first identify the coefficients of all the variable terms in the expression. The coefficient is the number that is multiplied by the variable.
Once we have identified the coefficients, we find the GCF of all the coefficients. The GCF is the largest number that can be evenly divided into all the coefficients without leaving a remainder.
After finding the GCF, we multiply it by the variable. This will give us the factor that we can factor out.
Steps for Factoring Out the Coefficient of the Variable
- Identify the coefficients of all the variable terms in the expression.
- Find the GCF of all the coefficients.
- Multiply the GCF by the variable.
- Factor out the product obtained in step 3 from the original expression.
Examples
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Factor out the coefficient of the variable in the expression 8x + 16y.
The coefficients of the variable terms are 8 and 16. The GCF of 8 and 16 is 8. Multiplying 8 by the variable x gives us 8x. Therefore, we can factor out 8x from the original expression, resulting in 8(x + 2y).
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Factor out the coefficient of the variable in the expression 12x^2 – 18x + 6.
The coefficients of the variable terms are 12, -18, and 6. The GCF of 12, -18, and 6 is 6. Multiplying 6 by the variable x gives us 6x. Therefore, we can factor out 6x from the original expression, resulting in 6(2x^2 – 3x + 1).
Conclusion
Factoring out the coefficient of a variable is a simple process that can be used to simplify mathematical expressions. By following the steps outlined above, you can easily factor out the coefficient of a variable and improve your understanding of algebra.
Are you interested in learning more about algebra?
If you are interested in learning more about algebra, there are many resources available to you. You can find books, websites, and even online courses that can teach you about this important branch of mathematics.
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