The product of prime polynomials [tex]\rm 3x(x-3)(x^2+3x+9)[/tex] is equivalent to
[tex]\rm 3x^4-81x[/tex].
It is given that the polynomial [tex]\rm 3x^4-81x[/tex].
The product of prime polynomials is equivalent to the above polynomial.
Polynomial is the combination of variables and constants in a systematic manner with "n" number of power in ascending or descending order.
We have:
[tex]\rm 3x^4-81x\\\rm 3x(x^3-27)\\\rm 3x(x^3-3^3)\\\rm 3x(x-3)(x^2+3x+3^2) \\\\ We \ know \ that \ a^3-b^3=(a-b)(a^2+ab+b^2)\\3x(x-3)(x^2+3x+9)\\[/tex]
Thus the option [tex]\rm 3x(x-3)(x^2+3x+9)[/tex] is correct.
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