Final answer:
To find the binomial that makes the expression 36x + 24 equivalent to its original form when multiplied by its greatest common factor (GCF), first find the GCF, which is 12, and then divide each term by the GCF. The result is the binomial 3x + 2.
Step-by-step explanation:
The student has asked to find the binomial that when multiplied by the greatest common factor completes the expression 36x + 24 to make it equivalent to its original form. To figure this out, one must first determine the greatest common factor (GCF) of the two terms in the expression, which is 12. This is because 12 is the highest number that divides both 36 and 24 without leaving a remainder.
So, we divide each term by the GCF to find the other factor, which is the binomial. When we divide 36x by 12 we get 3x, and when we divide 24 by 12, we get 2. Therefore, the binomial that we are left with is 3x + 2.