Factor the expression completely: 45bcx - 10ax
5x(9bc - 2a)
To factor the expression 45bcx - 10ax completely, we first identify the greatest common factor (GCF), which is 5x. Factoring this out results in the expression 5x(9bc - 2a), confirming that A is indeed the correct choice.
This choice correctly represents the fully factored form of the original expression. By taking out the GCF of 5x from both terms, we are left with the expression 9bc - 2a, which cannot be factored further.
While this option correctly factors out the number 5 from the expression, it neglects to include the variable x that is common to both terms of the original expression. Therefore, this choice does not accurately represent the complete factorization.
This choice mistakenly factors out only the variable x, leaving the coefficients unchanged. The expression inside the parentheses is not fully factored, as it can still be simplified by factoring out a common factor of 5. Hence, this does not provide the complete factorization of the original expression.
This option incorrectly includes a plus sign instead of a minus sign in the parentheses. The original expression requires a subtraction of 2a, making this choice incorrect. The sign is crucial for maintaining the equality of the original expression.
The correct factorization of the expression 45bcx - 10ax is 5x(9bc - 2a), which accurately reflects the greatest common factor extraction. Choices B, C, and D fail for various reasons, such as missing the variable x or incorrect signs, showcasing the importance of careful factorization in algebraic expressions.
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