math

1.) when the expression 4x^2-3x-8 is divided by x-a, the remainder is 2. find the value of a.

2.) the polynomial 3x^3+mx^2+nx+5 leaves a remainder of 128 when divided by x-3 and a remainder of 4 when divided by x+1. calculate the remainder when the polynomial is divided by x-3.

tnx...

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  1. let f(x) = 4x^2 - 3x - 8 and use the Remainder Theorem,

    f(a) = 4a^2 - 3a - 8 = 2
    4a^2 - 3a - 10 = 0
    (a-2)(4a + 5) = 0
    a = 2 or a = -5/4

    the 2nd is done the same way:
    f(3) = 81 + 9m + 3n + 5 = 128
    9m + 3n = 42
    3m + n = 14

    f(-1) = -3 - m - n + 5 = 4
    -m-n = 2

    add them:
    2m = 16
    m = 8 , then 24 + n = 14 ----> n = -10

    so f(x) = 3x^3 + 8x^2 -10x + 5
    f(3) = 81 + 72 - 30 + 5 = 128
    DUH, wasn't that given ?

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  2. thanks... :)

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