Equating Coefficients

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    Hey I'm new!
    I've recently started my AS-levels and have not yet been taught Co-efficient equating...
    Here it is:

    By equating coefficients find A, B and C: 18. 𝑥2−𝑥≡𝐴𝑥(𝑥+1)+ 𝐵𝑥19. 𝑥−4≡𝐴(2−𝑥)+𝐵( −3)

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    If someone could help me with this I would really appreciate it!

    Thank you.
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    So, if , then:
    Equating coefficients of :
    Equating coefficients of :
    Equating coefficients of :
    Equating coefficients of :
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    (Original post by metasysta)
    So, if , then:
    Equating coefficients of :
    Equating coefficients of :
    Equating coefficients of :
    Equating coefficients of :
    Okay so its mostly rearranging?

    My friend told me something about also solving it simultaneously.
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    (Original post by llamaha)
    Okay so its mostly rearranging?

    My friend told me something about also solving it simultaneously.
    It's not really rearranging so much. You basically expand everything on the RHS, collect the like terms (e.g. You would turn something like Ax+Bx^2+Cx into (A+C)x+Bx^2) and then you literally equate the coefficients and achieve equations which you can then solve. Some equations can have more than 1 variable for you to solve (such as the example I gave previously) therefore you would need another equation with the same unknowns in order to solve them simultaneously as your friend might've mentioned. This, of course, is not always the case as you would solve the single variable equations FIRST and see if you can use that information in double/triple/etc variable equations as well.

    So for 18, the RHS expanded fully would be Ax^2+(A+B)x and now you can compare the coefficients with LHS. As I previously mentioned, you can solve for the coefficient of x^2 first as that would give you the info you need for the coefficient of x
 
 
 
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