Final answer:
Upon simplification, none of the given polynomials are prime because they can all be factored into simpler expressions.
Step-by-step explanation:
The question asks which polynomial is prime. A prime polynomial is one that cannot be factored into the product of two non-constant polynomials. We are given four options:
- a) -4x + 3x + 2x + 6
- b) 3x - 2x - 6
- c) 10x - 4x + 3x + 6
- d) 10x - 10x + 6x - 6
To discern if a polynomial is prime, we need to first simplify each option:
- a) Simplifies to 1x + 6, which is not prime because it can be written as x(1) + 6.
- b) Simplifies to 1x - 6, which is not prime because it can be written as x(1) - 6.
- c) Simplifies to 9x + 6, which is not prime because it can be factored into 3(3x + 2).
- d) Simplifies to 6x - 6, which can be factored into 6(x - 1).
None of the given polynomials are prime as all can be factored into simpler expressions.