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    I'm just having a scroll through the June 2015 AQA Further Maths paper, and this one question has got me stumped:

    In the expansion of (x+2)(x^2+kx-3) the coefficient of x^2 is 0.

    a) work out the value of k
    b) work out the coefficient of x

    On a solutions paper, the answers are a) k=-2 and b) -7; I'm not sure how this was worked out, due to the method being completely different to what I would use when expanding.

    Could someone provide a small detailed explanation of how these results were obtained?

    Thanks.
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    Did you multiply out the brackets?
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    You should get:
    x^3 + kx^2 -3x + 2x^2 + 2kx - 6

    When it says that the coefficient of x^2 is 0, it basically means the number in front of the x^2.
    In the expression, you have kx^2 and 2x^2, and so k + 2 = 0. Therefore, k = -2
    To get the coefficient of x, use the value of k that you just found. You have two values in the expression: -3x and 2kx
    Since you know that k is -2, you can substitute thid in to get: -3x + (2*-2)x which simplifies to -7x.
    So the coefficient of x is 7
    Hope this helped! xx

    EDIT: theholychilli
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    Also, to expand the brackets, multiply everything in the second set of brackets by x, and then everything in the second set of brackets by 2
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    (Original post by surina16)
    You should get:
    x^3 + kx^2 -3x + 2x^2 + 2kx - 6

    When it says that the coefficient of x^2 is 0, it basically means the number in front of the x^2.
    In the expression, you have kx^2 and 2x^2, and so k + 2 = 0. Therefore, k = -2
    To get the coefficient of x, use the value of k that you just found. You have two values in the expression: -3x and 2kx
    Since you know that k is -2, you can substitute thid in to get: -3x + (2*-2)x which simplifies to -7x.
    So the coefficient of x is 7
    Hope this helped! xx

    EDIT: theholychilli
    Much appreciated! Thanks, I was thinking that it would be (0x^2+kx-3) in the bracket and it didn't occur to me that it is after you have expanded it. Thanks!
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    (Original post by theholychilli)
    Much appreciated! Thanks, I was thinking that it would be (0x^2+kx-3) in the bracket and it didn't occur to me that it is after you have expanded it. Thanks!
    No problem!
 
 
 
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