college algeb

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when ax^2+bx+c is divided by x-1, the remainder is 10 if the same poly. is divided by x+2 the remainder is 1. x+1 is a factor of the polynomial. Find a,b, and c.

  • college algeb -

    let f(x) = ax^2 + bx + c
    given f(1) = 10
    10 = a + b + c (#1)

    given f(-2) = 1
    1 = 4a - 2b + c (#2)

    given f(-1) = 0 , .... (it said x+1 is a factor)
    0 = a - b + c (#3)

    #1 - #3
    10 = 0 + 2b + 0
    b = 5

    #2 - #3
    1 = 3a - b + 0 , but b=5
    6 = 3a
    a = 2

    in #1
    2 + 5 + c = 10
    c = 3

    a=2, b=5, c=3

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