Answer:
(c) 12(2v-7)
Step-by-step explanation:
You want the expression resulting from factoring out the greatest common factor from the sum 24v -84.
The greatest common factor here is the GCF of 24 and 84. We note that ...
24 = 12·2
84 = 12·7
and 2 and 7 have no common factors. Then the GCF of 24 and 84 is 12.
The factored expression is ...
24v -84 = 12(2v -7)
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Additional comment
The GCF can also be found by considering the remainder from dividing 84 by 24. That remainder is 12, which divides both numbers with a remainder of 0. Hence 12 is the GCF.
If the remainder did not divide both numbers with a remainder of 0, then the process is repeated to find the GCF of the smaller number (24) and the remainder. (This is a description of Euclid's algorithm for finding the GCF.)
