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Math Help - help please :)

  1. #1
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    help please :)

    Identities Find values A, B and R

    X^2 - 2X + 7 = (x+3) (Ax + B ) + R


    thanks
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  2. #2
    GAMMA Mathematics
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    Quote Originally Posted by gracey View Post
    Identities Find values A, B and R

    X^2 - 2X + 7 = (x+3) (Ax + B ) + R


    thanks
    x^2 - 2x + 7 = (x+3) (Ax + B ) + R

    x^2 - 2x + 7 = Ax^2 +Bx + 3Ax + 3B + R

    (1-A)x^2 - (B+3A+2)x + (7-3B-R) =0

    Are you familiar with the quadratic formula?

    That will get you values of x. I now realized that you want the constants...

    x^2 - 2x + 7 = (x+3) (Ax + B ) + R

    Set x = -3

    9 + 6 + 7 = R

    R = 22

    Now, set x=0

    7 = 3B + R

    7 = 3B + 22

    B = -5

    I will leave A up to you.
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  3. #3
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    Have you considered multiplication?

    (x+3) (Ax + B ) + R = Ax^2 + (3A+B)x + (R+3B)

    Now match up the coefficients on the terms of equal degree.

    Don't use the quadratic formula. You are not solving for 'x'.
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  4. #4
    Super Member wingless's Avatar
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    Simply divide both sides by (x+3).

    x^2 - 2x + 7 = (x+3) (Ax + B ) + R

    \frac{x^2 - 2x + 7}{x+3}=\frac{(x+3) (Ax + B ) + R}{x+3}

    x-5 + \frac{22}{x+3} = Ax+B + \frac{R}{x+3}

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  5. #5
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    Quote Originally Posted by TKHunny View Post
    Have you considered multiplication?

    (x+3) (Ax + B ) + R = Ax^2 + (3A+B)x + (R+3B)

    Now match up the coefficients on the terms of equal degree.

    Don't use the quadratic formula. You are not solving for 'x'.
    This gives you A = 1, B = -5, R=22 matching what I gave.
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  6. #6
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    Quote Originally Posted by wingless View Post
    Simply divide both sides by (x+3).

    x-5 + \frac{22}{x+3}
    Notice that this requires a division algorithm. It isn't really magic if you put the complicated steps back in.
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  7. #7
    Super Member wingless's Avatar
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    Quote Originally Posted by TKHunny View Post
    Notice that this requires a division algorithm. It isn't really magic if you put the complicated steps back in.
    I don't think it's complicated. I can do it even without writing, anyone who knows division can do it too..
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