Find the approximate value of
$2 x^{3} + 3 x^{2} - 5 x + 7$ at $x = 2.05$

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Solution

$2 x^{3} + 3 x^{2} - 5 x + 7$
$= 2 (2.05)^{3} + 3 (2.05)^{2} - 5 (2.05) + 7$
$= 2 \times 8.6 + 3 \times 4.2 - 10.25 + 7$
$= 17.2 + 12.6 - 10.25 + 7$
$= 36.8 - 10.25$
$= 26.55$
$= 27$

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