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14 May, 05:55

Is (x - 4) a factor of f (x) = x3 - 2x2 + 5x + 1? Use either the remainder theorem or the factor theorem to explain your reasoning?

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  1. 14 May, 07:34
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    no

    Step-by-step explanation:

    The factor theorem states that if (x + h) is a factor of f (x) then f ( - h) = 0

    Given

    f (x) = x³ - 2x² + 5x + 1, then evaluating f (4)

    f (4) = 4³ - 2 (4) ² + 5 (4) + 1 = 64 - 32 + 20 + 1 = 53 ≠ 0

    Thus (x - 4) is not a factor of f (x)
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