Factor completely $6 x-18$
A. $6(x+3)$
B. $6(x-3)$
C. $6 x(-18)$
D. Prime
Answer (2)
Find the greatest common factor (GCF) of 6 x and − 18 , which is 6.
Factor out the GCF from the expression: 6 x − 18 = 6 ( x − 3 ) .
Check if the factored expression can be factored further. In this case, it cannot.
The completely factored form of 6 x − 18 is 6 ( x − 3 ) .
Explanation
Understanding the Problem We are asked to factor the expression 6 x − 18 completely. This means we want to find the greatest common factor (GCF) of the terms 6 x and − 18 and factor it out.
Finding the Greatest Common Factor The GCF of 6 x and − 18 is 6, since 6 is the largest number that divides both 6 x and − 18 . We can find this by finding the greatest common divisor (GCD) of the coefficients 6 and 18, which is 6.
Factoring out the GCF Now, we factor out the GCF, 6, from the expression 6 x − 18 . This gives us 6 ( x − 3 ) , since 6 x − 18 = 6 ( x ) − 6 ( 3 ) = 6 ( x − 3 ) .
Checking for Further Factoring We check if the factored expression 6 ( x − 3 ) can be factored further. Since x − 3 is a linear expression and has no common factors other than 1, the expression 6 ( x − 3 ) is completely factored.
Final Answer Comparing our result 6 ( x − 3 ) with the given options, we see that it matches the second option. Therefore, the completely factored form of 6 x − 18 is 6 ( x − 3 ) .
Examples
Factoring is a fundamental skill in algebra, and it's used in many real-world applications. For example, suppose you want to build a rectangular garden with an area of 6 x − 18 square feet. If you want the length to be 6 feet, you can factor the expression to find the width, which would be x − 3 feet. This helps you plan the dimensions of your garden efficiently.
The expression 6 x − 18 can be completely factored as 6 ( x − 3 ) . The greatest common factor of the terms is 6, which we factor out. Therefore, the correct option is B: 6 ( x − 3 ) .
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