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    how do i solve this:



    I know to get B we let x=1 and solve to get B=1/3

    But to get A and C do we have to equate coefficients?

    Would equating x terms give: -A + B - 2C = 0 ?
    and then equating constant terms: A + 2B + C = 1

    then we add the two to remove the x term then sub 1/3 in for B to allow us to get C.

    But I get that C=0?

    How can this be? What have i done wrong?
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    (Original post by Mr Tall)
    how do i solve this:



    I know to get B we let x=1 and solve to get B=1/3

    But to get A and C do we have to equate coefficients?

    Would equating x terms give: -A + B - 2C = 0 ?
    and then equating constant terms: A + 2B + C = 1

    then we add the two to remove the x term then sub 1/3 in for B to allow us to get C.

    But I get that C=0?

    How can this be? What have i done wrong?
    c has to be zero as c(1-x)^2 is the only term which has an x^2.
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    (Original post by steve44)
    c has to be zero as c(1-x)^2 is the only term which has an x^2.
    why does this mean it has to be zero? thanks
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    Expand out the brackets and equate x^2 terms.
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    A (1-x) + B (2+x) + C (1-x)^2 = 1

    becomes

    (A + 2B + C) + (-A + B -2C) x + C x^2 = 1

    In answer to your question about whether equating x terms gives -A + B -2C = 0 and equating constant terms gives A + 2B + C = 1... this is correct. Plus as there is no x^2 term on the RHS we can just immediately conclude C = 0.
 
 
 
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