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Math Help - Determine P(x) in Polynomials

  1. #1
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    Determine P(x) in Polynomials

    A monic polynomial P(x) of degree 3 satisfies the following conditions:

    x-1 divides P(x)+1 exactly
    x+1 divides P(x)-1 exactly
    and P(0)=1
    Determine P(x)
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  2. #2
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    Quote Originally Posted by nerdzor View Post
    A monic polynomial P(x) of degree 3 satisfies the following conditions:

    x-1 divides P(x)+1 exactly
    x+1 divides P(x)-1 exactly
    and P(0)=1
    Determine P(x)
    Your polynomial will be in the form: x^3 + ax^2 + bx + c

    P(x) = x^3 + ax^2 + bx + c

    P(0) = (0)^3 + a(0)^2 + b(0) + c = 1 \rightarrow c=1

    P(x)+1=0 when factor (x-1) is divided hence root is 1. Therefore, P(1) + 1 = (1)^3 + a(1)^2 + b(1) + 1 + 1 = 0 \rightarrow a+b+2 = 0.

    P(x)-1=0 when factor (x+1) is divided hence root is -1. Therefore, P(-1) + 1 = (-1)^3 + a(-1)^2 + b(-1) + 1 + 1 = 0 \rightarrow a-b+2 = 0.

    You have 2 simultaneous equation. Just got to solve for a,b and you will have your monic polynomial P(x).
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