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    Chapter: Algebraic Fractions
    Mixed Exercise 1E. Question 5.

    https://www.biochemtuition.com/wp-co...-fractions.pdf

    I can get the answer using long division, but how do i do it using the factor theorem.

    F(x)=(Ax^2+Bx+C)(X^2-1)+Dx+E

    Is that wrong, if so how do i do it?
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    Eww colour

    you let x^2 = 1 and the answer is C
    There you compare coefficients for B
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    (Original post by ValerieKR)
    Eww colour

    you let x^2 = 1 and the answer is C
    There you compare coefficients for B
    I got D = 3 not C is their something i'm doing wrong? Is it not correct to do F(x)=(Ax^2+Bx+C)(X^2-1)+Dx+E?
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    (Original post by Paranoid_Glitch)
    I got D = 3 not C is their something i'm doing wrong? Is it not correct to do F(x)=(Ax^2+Bx+C)(X^2-1)+Dx+E?
    Do you mean Q6, not Q5?
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    (Original post by ValerieKR)
    Do you mean Q6, not Q5?
    Alright now i know i'm messing something up. Still on Question 5, could you do the entire question?
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    (Original post by Paranoid_Glitch)
    Alright now i know i'm messing something up. Still on Question 5, could you do the entire question?
    Just use long division.
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    (Original post by RDKGames)
    Just use long division.
    Yeah i know how to. But the person i'm showing wants to know how to do it using the remainder theorem
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    (Original post by Paranoid_Glitch)
    Yeah i know how to. But the person i'm showing wants to know how to do it using the factor theorem
    The factor theorem just tests whether something is a factor of a function equaling 0. The remainder theorem will get you the remainder. Neither method will give you the full expression.
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    (Original post by Paranoid_Glitch)
    Alright now i know i'm messing something up. Still on Question 5, could you do the entire question?
    For Q5:

    x^4 + 2 = (x^2 - 1)(x^2 + B) + C - now expand and compare coefficients.
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    (Original post by Zacken)
    For Q5:

    x^4 + 2 = (x^2 - 1)(x^2 + B) + C - now expand and compare coefficients.
    Why just (X^2+B) and not (Ax^2 + Bx +C) ?
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    (Original post by Paranoid_Glitch)
    Why just (X^2+B) and not (Ax^2 + Bx +C) ?
    Are we looking at the same question?

    It say to find B,C such that \displaystyle \frac{x^4 +2}{x^2 - 1} = x^2 + B  + \frac{C}{x^2 - 1}. Multiply both sides by x^2 - 1 to turn it into a polynomial identity:

    \displaystyle x^4 + 2 = (x^2 - 1)(x^2 + B) + (x^2-1)\frac{C}{x^2 -1} = (x^2 -1)(x^2 + B) + C

    I'm really not sure where your A,B, C has come from...
 
 
 
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