Explain, in complete sentences, why the expression x2 – 12x – 36 is prime.

Question

anonymous · Answer

because you can't factor it. You can only factor x2-12x+36.
hope it helps!! 
:0)

hero · Answer

A quadratic polynomial is composite if it can be expressed as the product of prime factors, usually two binomials. 

A quadratic polynomial is prime because it cannot be expressed as the product of two prime binomials. 

Similarly, 9 is composite because it can be expressed as a product of 2 primes: 3 x 3
              5 is prime because it cannot be expressed as a product of 2 primes.

hero · Answer

@mscrosscountry

anonymous · Answer

if it has no roots it has no factors, therefore it is prime

anonymous · Answer

$$x^2 – 12x – 36=\left(x-6 \left(1-\sqrt{2}\right)\right)
   \left(x-6
   \left(1+\sqrt{2}\right)\right)
$$
so the polynomial is prime over the integer but not prime over the reals.

hero · Answer

@eliassaab , it asked to explain why the polynomial is prime, not why it is not prime over all reals.

anonymous · Answer

To have a precise answer, you need a precise question. The question should be is
this polynomial prime over the integer?
If this is the case, one can say that the polynomial is not prime since there is no
integers m and n, p and q so that
x^2 – 12x – 36= ( p x + m)( q x + n)
since this would imply that p=q=1$$
m=6(1-\sqrt 2)\
n=6(1+\sqrt 2)\
This is a contradiction since m and n are not integers.
$$