If f(x) = 5x3 + 4x2 – 13x – 25 and f(x–3) = 5x3 – 41x2 + 98x + k then k =

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If f(x) = 5x³ + 4x² – 13x – 25 and f(x–3) = 5x³ – 41x² + 98x + k then k =

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answer is -85.

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Detailed Solution

f(x) = 5x³ + 4x² – 13x – 25

$f (x - 3) = 5 (x - 3)^{3} + 4 (x - 3)^{2} - 13 (x - 3) - 25 = 5 (x^{3} - 27 - 9 x^{2} + 27 x) + 4 (x^{2} + 9 - 6 x) - 13 x + 39 - 25 = 5 x^{3} - 45 x^{2} + 135 x - 135 + 4 x^{2} - 24 x + 36 - 13 x + 39 - 25 = 5 x^{3} - 44 x^{2} + 98 x - 85$

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