Question

Which product of prime polynomials is equivalent to 3x4 – 81x?

3x(x – 3)(x2 – 3x – 9)
3x(x – 3)(x2 + 3x + 9)
3x(x – 3)(x – 3)(x + 3)
3x(x – 3)(x + 3)(x + 3)

Answer 1

It's B

Explanation:

Answer 2

Given:

The expression is

`3x^4-81x`

To find:

The product of prime polynomials which is equivalent to the given expression.

Solution:

We have,

`3x^4-81x`

Taking out the common factors, we get

`=3x(x^3-27)`

It can be written as

`=3x(x^3-3^3)`

`=3x(x-3)(x^2+3x+3^2)`
`[\because a^3-b^3=(a-b)(a^2+ab+b^2)]`

`=3x(x-3)(x^2+3x+3^2)`

`=3x(x-3)(x^2+3x+9)`

Therefore, the correct option is B.