Final answer:
The expression 24m - 12p + 72 is factored by dividing each term by their greatest common divisor, which is 12. This yields the equivalent expression 12(2m - p + 6), which is choice C in the given options.
Step-by-step explanation:
To factor the expression 24m - 12p + 72, we look for the greatest common divisor (GCD) that all three terms share. This GCD is 12, as all three terms can be divided evenly by 12. Division of each term by 12 gives us:
- 24m ÷ 12 = 2m
- -12p ÷ 12 = -p
- 72 ÷ 12 = 6
After factoring out the GCD (12), we rewrite the expression as:
12(2m - p + 6)
This is equivalent to choice C: 12(2m - p + 6). Therefore, the factorized expression is 12 times the sum of 2m, the negation of p, and 6. This is the only equivalent expression that maintains the same value as the original expression when the factor is distributed back across each term.