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Theodore and clear we're each asked to factor the term 24x to the fifth as the product of two monomials their responses are shown below so Theodore factored 24x to the fifth as being equal to 8x third times three x squared and Claire factor 24x to the fifth is being equal to four x times 6x to the fourth and then they ask us which of the students factored 24 X to the fifth correctly so I encourage you pause the video and see if you can figure out figure this out which of them factored it correctly alright now let's first look at Theodore so he factored it into these two monomials 8 X to the third + 3 x squared well let's just see if we were to multiply these two things do we get 24 X to the fifth so if you multiply 8 times 3 you do indeed get 24 and then all you have to do is multiply the X terms or the the X to the powers of X you have X to the 3rd times x squared that indeed does equal X to the 5th so Theodore did factor it correctly this is one factorization I guess you'd say of 24 X to the 5th now let's look at Claire so Claire if we were to take just the coefficients 4 times 6 is indeed equal to 24 and then if we were to look at the powers of X we have X to the first power here times X to the fourth power which is going to be X to the fifth power so Claire also factored it correctly and this just goes to show you that there's more than one possible factorization of a monomial like 24 X to the fifth I could come up with another one I could write something like 24 X to the fifth I could say that that is 12x I could write that as 12 X to the third times let's see what would have to be left 12 times 2 is 24 so 2x squared that's another possible factorization so clearly there's just more more than one way to factor this monomial into two other monomials