Question

Which polynomial is prime?

Answer 1

Answer:

$4x^4 + 2x^3 -2x + 4$ is a prime polynomial.

Step-by-step explanation:

Given some polynomials we have to choose the polynomial which is prime.

A prime polynomial is a polynomial with integer coefficients that cannot be factored lower degree polynomials or simply we can say prime polynomial is a polynomial that can't be factored.

Option A: $x^3+3x^2-2x-6$

$x^3+3x^2-2x-6=x^2(x+3)-2(x+3)=(x^2-2)(x+3)$

∴ can be factored as $(x+3)(x^2-2)$

Option B: $x^3+3x^2-2x-6$

$x^3+3x^2-2x-6=x^2(x+3)-2(x+3)=(x^2-2)(x+3)$

∴ can be factored as $(x^2-2)(x+3)$

Option C: $4x^4+4x^3-2x-2$

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

∴ can be factored as $2(x+1)(2x^3-1)$

Option D: $4x^4 + 2x^3 -2x + 4$

The above polynomial can't be factored.

Hence,  $4x^4 + 2x^3 -2x + 4$ is a prime polynomial.

Option D is correct.

Answer 2

One of the never answered. sad. its D.