Posted by T.Gracken on November 01, 2002 at 11:41:51:
In Reply to: factor this posted by jack on November 01, 2002 at 11:00:47:
: X^2-X+6
: What are the factors? I had this on a quiz today and totally blanked out.
when the coefficient of x2 is 1, all you need are two numbers that multiply to the constant and add to the coefficient of the middle.
that is, two numbers that multiply to +6 and same two numbers add to -1.
the only way we can factor +6 using two integers are
-1 and -6,
1 and 6,
-2 and -3,
2 and 3
since none of these pair add to -1, we conclude that the polynomial is prime (that is, it can not be factored using integers)