If $f (x) = 2 x^{3} + 3 x^{2} - 11 x + 6$ , find $f (- 3)$

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Solution

In the given polynomial $f (x) = 2 x^{3} + 3 x^{2} - 11 x + 6$ , substitute $x = - 3$ as shown below:

$f (- 3) = (2 \times (- 3)^{3}) + (3 \times (- 3)^{2}) - (11 \times (- 3)) + 6 = (2 \times (- 27)) + (3 \times 9) + 33 + 6 = - 54 + 27 + 33 + 6$
$= - 54 + 66 = 12$

Hence, $f (- 3) = 12$ .

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