Respuesta :
Given:
The expression is
[tex]3x^4-81x[/tex]
To find:
The product of prime polynomials which is equivalent to the given expression.
Solution:
We have,
[tex]3x^4-81x[/tex]
Taking out the common factors, we get
[tex]=3x(x^3-27)[/tex]
It can be written as
[tex]=3x(x^3-3^3)[/tex]
[tex]=3x(x-3)(x^2+3x+3^2)[/tex] [tex][\because a^3-b^3=(a-b)(a^2+ab+b^2)][/tex]
[tex]=3x(x-3)(x^2+3x+3^2)[/tex]
[tex]=3x(x-3)(x^2+3x+9)[/tex]
Therefore, the correct option is B.
