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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
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Quote:
 Originally Posted by Furai 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
after you multiply all that out you will have a polynomial in x of the form

$c_0 + c_1 x + c_2 x^2 + c_3 x^3 + c_4 x^4 + c_5 x^5$

$c_4$ 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
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Quote:
 Originally Posted by Furai 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
note that expanding $(x^2 + 2x +3)(x^2 + 7x - 2)$ yields a cubic term of $7x^3 + 2x^3 = 9x^3$ ... multiplying by the $x$ out front makes that cubic term a quartic term of $9x^4$

August 27th, 2016, 01:45 PM   #4
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 Originally Posted by skeeter note that expanding $(x^2 + 2x +3)(x^2 + 7x - 2)$ yields a cubic term of $7x^3 + 2x^3 = 9x^3$ ... multiplying by the $x$ out front makes that cubic term a quartic term of $9x^4$
So 9 would be the coefficient?

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