Dividing PolynomialsDate: 8/18/96 at 2:35:54 From: Anonymous Subject: Dividing Polynomials Please help me with this problem. I know what the answer is; I just can't seem to get the same solution. (a^3 - 6a^2 + 8a) ----------------- 5 -------------------------- (2a - 4)/(10a - 40) Thank you. Date: 8/30/96 at 15:47:51 From: Doctor James Subject: Re: Dividing Polynomials Okay, your problem is: ( [a^3 - 6a^2 + 8a]/5 )/( [2a - 4]/[10a - 40] ) The first thing to do is to remember (a/b)/(c/d) = (a/b)*(d/c). So we get: ( [a^3 - 6a^2 + 8a]/5 )*( [10a - 40]/[2a - 4] ) Factoring out a 2 from the top and bottom of the right side gives us: ( [a^3 - 6a^2 + 8a]/5 )*( [5a - 20]/[a - 2] ) Now, remeber that (a/b)*(d/c) = (a/c)*(d/b). So we can get: ( [a^3 - 6a^2 + 8a]/[a - 2] )*( [5a - 20]/5 ) But 5 goes into 5a and 20 nicely, leaving: ( [a^3 - 6a^2 + 8a]/[a - 2] )*(a - 4) Factoring out an a from the top of the left side leaves us with: ( a*[a^2 - 6a + 8]/[a - 2] )*(a - 4) but we can factor the a^2 - 6a + 8 to give us: ( a*[a - 2]*[a - 4]/[a - 2] )*(a - 4) But the (a - 2) on the top and bottom can cancel out! So we have: (a*[a - 4])*(a - 4) or: a*(a - 4)^2 = a^3 - 8a^2 + 16a, which should be the answer. -Doctor James, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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