Determine whether the given binomial is a factor of the polynomial p(x) . p(x)=x^ 3 +2x^ 2 -x-2;(x+2)

isn't a factor of the polynomial .

Step-by-step explanation:

By the Factor Theorem, for any constant , would be a factor of a polynomial if and only if is a root (a zero) of that polynomial (.)

In other words, is a factor of polynomial if and only if replacing all mentions of in with the constant would yield .

For example, in this question, could be rewritten as (value of the constant is .)

By the Factor Theorem, would be a factor of the polynomial if and only if replacing all mentions of in with evaluates to .

Replacing all mentions of in with gives:

.

Simplify:

.

Since , (or equivalently, ) is indeed a factor of the polynomial .

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step-by-step explanation: