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

Answer:

Product of prim polynomials is $4x^{5}-6x^{4}+4x^{3}-6x^{2}$

Step-by-step 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 $2x^{2}(x^{2}+1)(2x-3)$.