Thank you, MrAl.
So I think I had it wrong from the start. Actually the polynomial x^2+7x-6 is not factorable over integers but it is factorable over real numbers. And whether a polynomial is factorable over real numbers (which also include integers) is determined by the discriminant b^2-4ac; if the discriminant is negative then the polynomial is not factorable over real numbers.
Now I must rephrase what I said earlier.
Q1: A polynomial of the type x^2+7x-6 is not factorable over integers. I have always thought whenever there is such a case that a polynomial is not factorable over integers then the coefficient of the 'x' term would be a prime number but still that does not mean whenever the coefficient of 'x' term is a prime, it's not factorable. For instance, the coefficient of 'x' term in the polynomial, x^2+3x+2, is prime but it's still factorable. But still whenever a polynomial is not factorable over integers, the coefficient of 'x' term is going to be a prime. Do I have it correct? Please let me know. Thank you.
Q2: Is there a simple way to tell if a quadratic polynomial is not factorable over integers by just looking at the coefficients?
Please help me. Thanks.
Regards
PG
You are posing an interesting mathematical question, but I think you need to clarify the mathematical statement better. Are you talking about polynomials of the form ax^2+bx+c where a, b and c are integers? And, if so, are you trying determine when you can factor this into a product (dx+e)(fx+g), where d, e, f and g are integers? Or, is it something a little different than that?
I think i can come up with one in about five minutes
Are you talking about a general algorithm, or one specific involving prime numbers or other restrictions? I'm not following what you mean by algorithm1 and algorithm2.
I'm talking about a general algorithm, and one for a person to use directly without computer. If you can find a general algorithm in 5 minutes, then this will be the answer PG is looking for, i think.
Without restrictions (other than being integers) what "test" or "algorithm" can we do on a, b and c to know that integer values of d,e,f and g can be found.
Hi,
I was talking about an algorithm2 that checks algorithm1 to make sure algorithm1 really works. This is where algorithm1 is the one where we determine if it is possible for an integer factorization. Algorithm2 can be on a computer just to make sure algo1 works all the time.
Hello again,
Anyone that can pick up a calculator can solve this immediately by using the quadratic formula, so i dont see why we just dont do that.
Here is another test quadratic to consider
6144x^2+3904x+312=(96x+52)(64x+6)
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