Once the signs are determined all that remains is to fill in the two blanks. Look at all of the pairs of factors of the constant term. These pairs will be the candidates for the blanks. For example, if the constant term is 12, you will need to consider 1 and 12, 2 and 6, and 3 and 4. If both signs in the factors are the same, these will be the only ones you need to try. If the signs are different, you will need to reverse the order: 1 and 12 as well as 12 and 1; 2 and 6 as well as 6 and 2; 3 and 4 as well as 4 and 3. Try the FOIL method on these pairs. (Not every trinomial can be factored in this way.)
Examples
Examples
x2 – 2x –
15
Factors to check: .JPG){kind=small}
; and 
(works).
x2 – 11x +
18
Factors to check: 
, and 
(works).
x2 + 8x +
7
Factors to check: (x
+ 1)(x + 7) (works).
Practice
Factor the quadratic
polynomial.
Solutions
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