Which polynomial is prime? x3 + 3x2 – 2x – 6 x3 – 2x2 + 3x – 6 4x4 + 4x3 – 2x – 2 2x4 + x3 – x + 2

In this exercise we have to use the knowledge of prime polynomials to find what cannot be factored, so we have;

A) Can be factored.

B) Can be factored.
C) Can be factored.
D) Can't be factored.

Is a base form of a polynomial in other words is a polynomial that can't be factored.

So we have to:

A)

B)

C)

D)

See more about prime polynomials at link

A prime polynomial is a polynomial that can't be factored.

In order to check which polynomial is prime, we need to check which polynomials could be factored.

x^3 + 3x^2 – 2x – 6 can be factored as (x+3)(x^2-2)

x^3 – 2x^2 + 3x – 6 can be factored as (x-2)(x^2+3)

4x^4 + 4x^3 – 2x – 2 can be factored as 2(x+1)(2x^3-1)

2x^4 + x^3 – x + 2 can't be factored.

Therefore, 2x^4 + x^3 – x + 2 is a prime polynomial.

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