TO FACTOR WHEN CONSTANT TERM POSITIVE OR NEGATIVE
TO FACTOR x2 + bx + c WHEN IS POSITIVE
When the constant term of a trinomial is positive, look for two numbers with the same sign. The sign is that of the middle term:
x2 – 7x + 10 = (x – 2) (x – 5);
x2 + 7x + 10 = (x + 2) (x + 5).
TO FACTOR x2 + bx + c WHEN IS NEGATIVE
When the constant term of a trinomial is negative, look for two numbers whose product is negative. One must be positive and the other negative:
x2 – 4x – 21 = (x + 3) (x – 7);
x2 + 4x – 21 = (x – 3) (x + 7).
Consider pairs of numbers for which the number with the larger absolute value has the same sign as b, the coefficient of the middle term.