Algebra

Use the Factor Theorem to determine whether x+2 is a factor of P(x)=2x^4+x^3-3x-9.

Specifically, evaluate P at the proper value, and then determine whether x+2 is a factor.

P(__)=

x+2 is or is not a factor of P(x)____

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  1. The factor theorem states that a polynomial f(x) has a factor (x − k) if and only if f(k) = 0.

    So if (x+2) is a factor of P(x), then
    P(-2)=0.

    Since P(-2)= 21, it is clear that (x+2) is not a factor of P(x)=2x^4+x^3-3x-9.

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