Question

Which product of prime polynomials is equivalent to 4x5 – 6x4 + 4x3 – 6x2?

Answer 1

4 x^5 - 6 x^4 + 4 x³ - 6 x² =
Answer: 1 ) 2 x² ( x² - 1 ) ( 2 x - 3 )

Answer 2

Product of prim polynomials is
`4x^(5)-6x^(4)+4x^(3)-6x^(2)`

Explanation:

The given expression is
`4x^(5)-6x^(4)+4x^(3)-6x^(2)`

We have to find out the prime polynomials, the product of which is the given expression.

To find those polynomials we will find the prime factors of the expression.

`4x^(5)-6x^(4)+4x^(3)-6x^(2)=2x^(4)(2x-3)+2x^(2)(2x-3)`

`=(2x^(4)+2x^(2))(2x-3)`

`=2x^(2)(x^(2)+1)(2x-3)`

Therefore the product of prime polynomials is
`2x^(2)(x^(2)+1)(2x-3)`.