Factor the expression completely:
$45 b c x-10 a x$
Answer (2)
Identify the greatest common factor (GCF) of the terms: The GCF of 45 b c x and − 10 a x is 5 x .
Factor out the GCF from both terms: 45 b c x − 10 a x = 5 x ( 9 b c − 2 a ) .
The expression 9 b c − 2 a cannot be factored further.
The completely factored expression is: 5 x ( 9 b c − 2 a ) .
Explanation
Understanding the Problem We are asked to factor the expression 45 b c x − 10 a x completely. This means we want to find the greatest common factor (GCF) of the two terms and factor it out.
Finding the Greatest Common Factor (GCF) First, let's identify the factors of each term:
45 b c x = 3 × 3 × 5 × b × c × x
10 a x = 2 × 5 × a × x
Now, let's find the common factors of both terms. Both terms have a factor of 5 and a factor of x . Therefore, the greatest common factor (GCF) is 5 x .
Factoring out the GCF Next, we factor out the GCF, 5 x , from each term:
45 b c x − 10 a x = 5 x ( 9 b c − 2 a )
Final Factored Expression The expression 9 b c − 2 a cannot be factored further, so the completely factored expression is 5 x ( 9 b c − 2 a ) .
Examples
Factoring expressions is a fundamental skill in algebra and is used in many real-world applications. For example, if you are designing a rectangular garden with an area represented by the expression 45 b c x − 10 a x , where x is the width of the garden, and you want to find the possible dimensions of the garden in terms of a , b , and c , you would need to factor the expression. Factoring helps you rewrite the area as a product of simpler expressions, which can represent the length and width of the garden. In this case, the factored form 5 x ( 9 b c − 2 a ) tells you that one possible width is x and the corresponding length is 5 ( 9 b c − 2 a ) .
To factor the expression 45 b c x − 10 a x completely, we find the greatest common factor, which is 5 x , and rewrite the expression as 5 x ( 9 b c − 2 a ) . The term 9 b c − 2 a cannot be factored further. Therefore, the completely factored form is 5 x ( 9 b c − 2 a ) .
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