Question

Which polynomial is prime?

A)x3 + 3x2 – 2x – 6
B)x3 – 2x2 + 3x – 6
C)4x4 + 4x3 –2x – 2
D)4x4 + 2x3 –2x + 4

Answer 1

one of the never answered. sad. its D.

Answer 2

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

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.