Question

Which polynomial is prime?

Answer 1

Answer:

None

Step-by-step explanation:

Prime polynomial : It is defined as that polynomial which can not be factorized into polynomial of lower degree , also with integer coefficient .

1.$3x^3+3x^2-2x-2$

$3x^2(x+1)-2(x+1)$

$(x+1)(3x^2-2)$

$(x+1)(\sqrt 3x+\sqrt2)(\sqrt3x-\sqrt2)$

It is not prime polynomial because it can be factorized into polynomial of lower degree.

2.$3x^3-2x^2+3x-4$

$(x-1)(3x^2+x+4)$

It is not a prime polynomial because it can be factorized into polynomial of lower degree.

3.$4x^3+2x^2+6x+3$

$2x^2(2x+1)+3(2x+1)$

$(2x+1)(2x^2+3)$

It is not prime polynomial because it can be factorized into polynomial of lower degree.

4.$4x^3+4x^2-3x-3$

$4x^2(x+1)-3(x+1)$

$(x+1)(4x^2-3)$

It is not a prime polynomial because it can be factorized into polynomial of lower degree.

Answer:None

Answer 2

Answer:

4x3+2x2+6x+3 is the prime polynomial