If the degree of the polynomial $6 x^{3} + x^{a - 4} + x^{2} + 101$ is 5, then the value of $a$ is

1

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3

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5

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9

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Solution

The correct option is D $9$
Given that the degree of the polynomial $6 x^{3} + x^{a - 4} + x^{2} + 101$ is 5.
The highest known power is the power of $x^{3}$ which is $3$ .
Therefore the $a - 4$ has to be $5$ in order for that to be the degree of the polynomial.
$\Rightarrow a - 4 = 5$
$\Rightarrow a = 5 + 4 = 9$

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