If $f (x) = x^{3} - 2 x^{2} + 7 x + 5$ , then $f (x - 2) =$

x^{3} + 8 x^{2} + 27 x - 25

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x^{3} - 8 x^{2} + 27 x - 25

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x^{3} + 8 x^{2} + 27 x + 25

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x^{3} - 8 x^{2} - 27 x + 25

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Solution

The correct option is A $x^{3} - 8 x^{2} + 27 x - 25$
Given, $f (x) = x^{3} - 2 x^{2} + 7 x + 5$
Replacing $x \to x - 2$ int he given expression,
$f (x - 2) = {(x - 2)}^{3} - 2 {(x - 2)}^{2} + 7 (x - 2) + 5 = x^{3} - 8 - 3. x .2 (x - 2) - 2 (x^{2} + 4 - 4 x) + 7 (x - 2) + 5 = 0 = x^{3} - 8 - 6 x^{2} + 12 x - 2 x^{2} - 8 + 8 x + 7 x - 14 + 5 = x^{3} - 8 x^{2} + 27 x - 25$

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