Math

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The quotientire and reminder are x-2 and -2x+4 respectively when the polynomial x^3-3x^2+x+2 is divided by g(x) find g (x).

  • Math -

    well, the highest power is 2 to get x-2 out of this

    (1x^3-3x^2+1x+2)/(ax^2+bx+c)
    =
    [ x - 2 + (-2x+4)/(ax^2+bx+c)]
    so multiply
    [ x - 2 + (-2x+4)/(ax^2+bx+c)]
    by (ax^2+bx+c)
    = -2x+4
    -2 (ax^2+bx+c)
    +x (ax^2+bx+c)

    = 4-2c
    -2x-2bx+cx
    -2ax^2+bx^2
    +ax^3
    which has to be x^3-3x^2+x+2
    so
    a = 1

    -3 = -2+b
    so
    b = -1

    1 = -2 -2(-1)+c
    1 = c
    so try
    g(x) = x^2-x+1

  • Math -

    check it
    (It works :)

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