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Math Help - Help with functions or whatever it's name is

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    Help with functions or whatever it's name is

    Hello guys, i've got this report i have to do and would really need your help.. This will propably be a piece of cake for you guys. Here it is:

    Which value for the constant a is the polynom Q(x)=2ax^3-x+a^2 divideable with
    a) x+1 b)2x+1
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    Quote Originally Posted by FelluRan View Post
    Hello guys, i've got this report i have to do and would really need your help.. This will propably be a piece of cake for you guys. Here it is:

    Which value for the constant a is the polynom Q(x)=2ax^3-x+a^2 divideable with
    a) x+1 b)2x+1
    Use the factor theorem: If (x-p) is a factor of f(x) then f(p) = 0

    Q(-1) = 2a(-1)^3-(-1)+a^2 = a^2-2a+1 = (a-1)^2 = 0

    \therefore a = 1
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    Could you please write more specificly what you have done ? (I know i'm stupid )
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    Factor theorem - Wikipedia, the free encyclopedia

    Q(x)=2ax^3-x+a^2

    The factor theorem says that (x-p) is a factor of f(x) only if f(p) = 0

    As the question says find the value of a for which x+1 is a factor of Q(x) this means the factor theorem is applied and so Q(-1) = 0

    This means we find the value of Q(-1) by substituting -1 wherever x is seen and setting Q(x) to 0

    Q(-1) = 2a(-1)^3 -(-1) + a^2 = 0

    This simplifies to a^2-2a+1=0 which in turn simplifies to (a-1)^2 = 0 and hence it's clear that a = 1
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    To be precise, a = 1 found in this way is the necessary, but not automatically sufficient, condition for Q(a, x) to be divisible by x + 1. Therefore, to show that it is sufficient, one can actually verify that x + 1 divides Q(1, x) with no remainder.
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