Question

Which term can be added to the list so that the greatest common factor of the three terms is 12h3?

36h3, 12h6, __________

6h3
12h2
30h4
48h5

Answer 1

if the GCF of all three terms must be 12 h^3 then:

1. the missing term must contain h to the power of at least 3, but less than 6. why? because if it has, say, an h^2 term, then the GCF becomes h^2 instead of h^3, and if it has a term of h^6, then the GCF is h^6
2. the coefficient must have 12 as its greatest factor. using this logic, 24, 36, etc. wouldn't be acceptable coefficients because these have factors greater than 12. likewise, something less than 12 wouldn't work because it lacks 12 as a factor altogether

putting all this together, see if any answer choices fulfill all these conditions