Question 14

5x(9bc - 2)

Factoring the expression 45bcx - 10ax gives us 5x(9bc - 2). This represents the expression in its simplest factored form, highlighting the common factors.

A) 5x(9bc - 2)

This option is correct as it accurately represents the factored form of the expression. By factoring out the greatest common factor, which is 5x, we are left with 9bc - 2, confirming that this is indeed the complete factorization.

B) 5(9bc - 2)

Option B is incorrect because it omits the variable x from the factorization. While it correctly factors out 5, it fails to account for the x present in the original expression, thus making it an incomplete representation.

C) x(45bc - 10a)

This option is incorrect as it does not simplify the expression correctly. Although it does factor out x, it does not reduce the coefficients properly, keeping them at 45 and -10 instead of factoring out the greatest common factor of 5.

D) 5x(9bc + 2)

Option D is also incorrect because it incorrectly uses a plus sign inside the parentheses. The original expression requires a subtraction, as evidenced by the negative coefficient of -10a, leading to a misrepresentation of the expression.

Conclusion

The correct answer, 5x(9bc - 2), effectively captures the complete factorization of the original expression by correctly identifying and factoring out the greatest common factor. All other options either misrepresent the factorization or fail to include all necessary components, thus confirming the accuracy of option A.