Factoring FractionsDate: 12/7/95 at 19:12:41 From: Anonymous Subject: dividing polynomials by monomials 12ax+16x ________ = ? 4x I just don't understand how to do this. Date: 12/23/95 at 22:28:55 From: Doctor Elise Subject: Re: dividing polynomials by monomials Hi! The best way to tackle this one is to try factoring the first polynomial. You start with 12ax + 16x The first thing I notice, is that both expressions have an 'x' in them, so we can pull it out like this: x(12a + 16) (I've grouped the expressions together and multiplied the group by 'x', after dividing each expression by 'x'). Next, I look at 12 and 16, (especially since I already know I have to divide by 4x) and realize they're both divisible by 4, so I can pull the 4 out the same way, and I get: 4x(3a + 4) Now the problem is easy, because I have 4x times something divided by 4x, and the 4x's cancel each other out (because anything divided by itself is 1) so I end up with 4x(3a + 4) __________ = 3a + 4 4x Does this help? Whenever you get a problem like this, the first thing to try is to see if the part you're dividing by (the '4x', in this case) is a factor of each expression in the numerator. You'd do the same thing if you had (3 * 2 * 5) + (3 * 7) ___________________ 3 You'd know to look for '3' as a common factor in each expression. Extra Credit: Can you find the answer to the problem I just posed? - Doctor Elise, The Geometry Forum |
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