Respuesta :
The options that are prime polynomials are,
15x^2 +10x -9x+7, 8x^3+20x^2+3x+12 and 11x^4+4x^2-6x^2-16
What is the prime polynomial?
A polynomial with integer coefficients that cannot be factored into polynomials of lower degree, also with integer coefficients, is called an irreducible or prime polynomial.
To determine all options in order to check that the polynomials are prime or not:
1). 15x^2 +10x -9x+7
5x(3x + 2) - (9x - 7)
Therefore, this polynomial can not be factored into lower degree polynomial. Therefore, it is a prime polynomial.
2). 20x^2-12x+30x-18
4x(5x - 3)+6(5x-3)
(4x + 6)(5x - 3)
Therefore, this polynomial is converted into a lower degree polynomial. Therefore, it is not a prime polynomial.
3). 6x^3+14x^2-12x-28
2x^2(3x+7)-4(3x+7)
(2x^2-4)(3x+7)
Therefore, this polynomial is converted into a lower degree polynomial. Therefore, it is not a prime polynomial.
4). 8x^3+20x^2+3x+12
4x^2(2x+5)+(3x+20)
Therefore, this polynomial can not be factored into lower degree polynomial. Therefore, it is a prime polynomial.
5). 11x^4+4x^2-6x^2-16
x^2(11x^2+4)-2(3x^2+8)
So, this polynomial can not be factored into lower degree polynomial. Therefore, it is a prime polynomial.
To learn more about the prime polynomial visit:
https://brainly.com/question/16749843
