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Which polynomial is prime?

a) -4x + 3x + 2x + 6
b) 3x - 2x - 6
c) 10x - 4x + 3x + 6
d) 10x - 10x + 6x - 6

User Bjornars
by
9.1k points

1 Answer

3 votes

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.

User Shb
by
7.9k points

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