Factor the expression completely: -3x - 21

Rationale

-3(x+7)

To factor the expression -3x - 21 completely, we can first factor out the greatest common factor, which is -3. This leaves us with the expression -3(x + 7), demonstrating the complete factorization.

A (-3(x+7)) CORRECT

This choice correctly represents the factored form of the expression -3x - 21. By factoring out -3, we simplify the expression to -3 times the quantity (x + 7), which accurately reflects the original expression when expanded.

B (-3(x-21)) YOUR ANSWER

This option incorrectly suggests that the expression can be factored to -3 times (x - 21). If expanded, this would yield -3x + 63, which does not match the original expression of -3x - 21.

C (-3(x-7)) YOUR ANSWER

This choice indicates the factorization as -3 times (x - 7). However, expanding this would result in -3x + 21, which again does not correspond to the original expression of -3x - 21.

D (-3(x+21)) YOUR ANSWER

This option implies that the expression can be factored to -3 times (x + 21). When expanded, this gives -3x - 63, which is incompatible with the original expression of -3x - 21.

Conclusion

The correct factorization of the expression -3x - 21 is -3(x + 7). This choice accurately captures the greatest common factor and retains the integrity of the original expression upon expansion. The other options fail to represent the correct factors, yielding expressions that do not match -3x - 21. Proper factorization is essential for simplifying algebraic expressions and solving equations effectively.

Factor the expression completely: -3x - 21

-3(x+7)

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