The degree of the polynomial obtained when $x^{3} - 2 x^{2} + 23$ is subtracted from $- 18 x^{2} - 2 x + x^{3} - 14$ is ________.

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Solution

The correct option is C 2
$(- 18 x^{2} - 2 x + x^{3} - 14) - ((x^{3} - 2 x^{2} + 23)$
$= (x^{3} - x^{3}) - (18 x^{2} - (- 2 x^{2})) - (- 2 x) - (23 - 14)$
$= (- 16 x^{2} - 2 x - 9)$
The degree of the resulting expression is 2, since the largest exponent is 2 in the resulting expression.

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