Which polynomials are prime? Check all that apply.
15x2 + 10x – 9x + 7
20x2 – 12x + 30x – 18
6x3 + 14x2 – 12x – 28
8x3 + 20x2 + 3x + 12
11x4 + 4x2 – 6x2 – 16
To determine if a polynomial is prime or not, we need to check if it can be factored further.
15x^2 + 10x - 9x + 7 = 15x^2 + x + 7
This polynomial cannot be factored any further, so it is prime.
20x^2 - 12x + 30x - 18 = 20x^2 + 18x - 18
This polynomial can be factored: 2(10x^2 + 9x - 9). Therefore, it is not prime.
6x^3 + 14x^2 - 12x - 28 = 2(3x^3 + 7x^2 - 6x - 14)
This polynomial can be factored: 2(3x + 2)(x^2 + 3x - 7). Therefore, it is not prime.
8x^3 + 20x^2 + 3x + 12
This polynomial cannot be factored any further, so it is prime.
11x^4 + 4x^2 - 6x^2 - 16 = 11x^4 - 2x^2 - 16
This polynomial can be factored: (11x^2 - 8)(x^2 + 2). Therefore, it is not prime.
Therefore, the prime polynomials are 15x^2 + 10x - 9x + 7 and 8x^3 + 20x^2 + 3x + 12.