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Show that (x + 4), (x – 3) and (x – 7) are factors x3 − 6x2 − 19x + 84.

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Let f(x) =x3 − 6x2 − 19x + 84 be the given polynomial 

In order to prove that (x+4), (x-3) and (x-7) are factors of f(x), it is sufficient to prove that f(-4) = 0, f(3) = 0 and f(7) = 0 respectively.

Hence, (x + 4), (x – 3) and (x – 7) are factors of given polynomial x3 − 6x2 − 19x + 84.

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