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Which of the following is a cubic polynomial?

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p (x) = y^{3} - 27

p (y) = x^{3} - 27

p (x) = x^{3} - 27

p (y) = 27

answer is C.

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Detailed Solution

Cubic polynomial is the polynomial in which the highest power of the unknown variable is 3.

p (x) = a x^{3} + b x^{2} + cx + d

For example

P (x) = x^{3} - 5 x^{2} + 15 x - 6

Option (1); The polynomial given in this option is,

p (x) = y^{3} - 27

Here, the polynomial is of x. For this polynomial to be cubic, there should be one term such that

a x^{3}

available.
As there is no such term. Hence, this is not cubic polynomial.
Option (2): The polynomial given in this option is,

p (y) = x^{2} - 27

In this polynomial unknown variable is y. As there is no term

a y^{3}

is there. Hence, the given function is not cubic polynomial. Option (3); The polynomial given in this option is,

p (x) = x^{3} - 27

Here, the polynomial is in x and there is one term. If we compare this with stationed form

p (x) = a x^{3} + b x^{2} + cx + d, we get

a = 1, b = 0, c = 0

and

d = - 27

Here one term of

a x^{3}

is present, so the given polynomial is cubic polynomial.
Option (4): The polynomial given in this option is,

p (y) = 27

Here the polynomial is in y. The highest power of y is 0. So, this is not cubic polynomial.
Thus, option 3 is correct.

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