Determine if x - 2 is a factor of p(x) = x^4 - 3x^2 + 2x - 8, and explain why.

(x-2) is a factor of the given p(x).

Step-by-step explanation:

A general polynomial

can be written as a product of factors

where

are roots of that polynomial.

In the case given in this problem, we have the polynomial

and if we evaluate

we confirm that 2 is a root of this polynomial. Therefore, as it could be expressed as a factor of binomials with its roots, we can ensure that (x-2) is a factor of p(x).

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step-by-step explanation:

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