Degree of the polynomial $(a^{2} - 1) (a + 2) (a^{3} + 3)$ is

3

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6

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2

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7

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Solution

The correct option is A $6$
Simplifying the given polynomial as follows:

$(a^{2} - 1) (a + 2) (a^{3} + 3) = (a^{3} + 2 a^{2} - a - 2) (a^{3} + 3) = a^{6} + 3 a^{3} + 2 a^{5} + 6 a^{2} - a^{4} - 3 a - 2 a^{3} - 6$
$= a^{6} + 2 a^{5} - a^{4} + a^{3} + 6 a^{2} - 3 a - 6$

Since the highest power of the polynomial $a^{6} + 2 a^{5} - a^{4} + a^{3} + 6 a^{2} - 3 a - 6$ is $6$ , hence the degree of the polynomial $(a^{2} - 1) (a + 2) (a^{3} + 3)$ is $6$ .

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