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August 27th, 2016, 01:08 PM  #1 
Newbie Joined: Aug 2016 From: England Posts: 3 Thanks: 0  Find the coefficient of x^4 in the expansion...
Evening guys, ok so i have a problem that has me stumped, i have been taking a look at it for quite some time whilst drinking my coffee and i am still not sure what theorem or method to use to solve it other than the fact that it obviously requires some form of expanding/simplifying algebra. The question itself: Find the coefficient of x^4 in the expansion of: x(x^2 + 2x +3)(x^2 + 7x  2) Am not sure how i am meant to identify the coefficient of x^4. Any help would be appreciated PS: Am not sure if this is the right section for this post, please feel free to move it to the correct section if it is necessary 
August 27th, 2016, 01:27 PM  #2  
Senior Member Joined: Sep 2015 From: USA Posts: 2,091 Thanks: 1087  Quote:
$c_0 + c_1 x + c_2 x^2 + c_3 x^3 + c_4 x^4 + c_5 x^5$ $c_4$ is the coefficient of $x^4$ You have two ways of going about it a) just do the multiplication and combine terms of the same power of x to obtain the form above and then just read off $c_4$ b) try and be a bit more clever by determining ahead of time which multiplications will end up with $x^4$ and just combining those terms. If I was dumping it into software I'd do (a). If I was doing it by hand I'd do (b)  
August 27th, 2016, 01:31 PM  #3  
Math Team Joined: Jul 2011 From: Texas Posts: 2,767 Thanks: 1422  Quote:
 
August 27th, 2016, 01:45 PM  #4 
Newbie Joined: Aug 2016 From: England Posts: 3 Thanks: 0  

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coefficient, expansion, find 
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