Question 18

-3(x+7)

The expression -3x - 21 factors to -3(x + 7) by taking out the common factor of -3 from both terms. This shows that the expression can be simplified neatly into a product of a constant and a binomial.

A) -3(x+7)

This option is correct because factoring -3 out of -3x gives x, and factoring -3 out of -21 gives +7, resulting in the expression -3(x + 7). This matches the original expression perfectly when expanded.

B) -3(x-21)

This option is incorrect because factoring -3 out of -3x would yield x, and factoring -3 out of -21 would result in -7, not -21. Therefore, this expression does not correspond to the original expression when expanded.

C) -3(x-7)

This option is also incorrect. If we factor -3 from -3x, we get x, and from -21, we would get +7, not -7. Thus, this choice does not accurately represent the factored form of the original expression.

D) -3(x+21)

This option is incorrect as well. Factoring -3 from -3x gives x, and factoring -3 from -21 gives -7, not +21. Hence, this expression does not match the original expression when expanded.

Conclusion

The correct answer, -3(x + 7), accurately factors the expression -3x - 21 by extracting the common factor of -3 and correctly represents the relationship between the factors. All other options fail to produce the correct terms when expanded, thus confirming that they do not represent the factored form of the original expression.