Answer: first, second and fourth are primes, the third is not-prime.
Step-by-step explanation:
A prime polynomial can not be reduced.
Let's see the options:
A) 6x^3 - 5x^2 + 2^x-14
You can see that we have a coefficient equal to 5 and other equal to 2.
As both are prime numbers, we can not reduce this, so this is a prime polynomial.
B) 12x^4 - 18x^2 + 8x^2 - 12 = 12x^4 -10*x^2 + 124
Both coefficients are even, so we can reduce it to:
12x4 -10*x^2 + 124 = 2*(6x^4 -5*x^2 + 72)
So this is not prime.
C) 6x^3 + 9x^2 + 10x + 15
we have that:
6 = 3*2
9 = 3*3
10 = 2*5
15 = 3*5
a polinomial is only reducible if all the coefficients share at least one prime factor, here we can see that this is not the case, so this is a prime polinomial.
D) 12x^2 -3x + 4x + 7 = 12x^2 + x + 7
Again, here we have that one coefficient is 1, the only factor of 1 is itself, so we can not reduce this polinomial, this is prime.
