Write two parentheses for the solution. That is, write ( )( ).
Determine the signs between the two binomials. If the integer for c is negative, one sign is negative and one sign is positive. If c and b are positive, both signs are positive. If c is positive but b is negative, both signs are negative. For (3x^2 - 70x + 23), write ( - )( - ).
Write the term for "ax" in the first spot in the first parenthesis and an x in the first spot of the second parenthesis. For example, write (3x- )(x- ).
Write the integer for c in the second spot in the first parenthesis and a 1 in the second spot of the second parenthesis. For the example, write (3x - 23)(x - 1).
Check the answer to complete the "guess and check" process. Multiply the first terms, the outer terms, the inner terms, and then the last terms and add the answers. For the example, 3x times x is 3x^2, 3x times -1 is -3x, -23 times x is -23x and -23 times -1 is 23. Thus, (3x^2 - 3x - 23x + 23) equals (3x^2 - 26x + 23) and is incorrect.
Swap the last term in each parenthesis, if needed, and recheck the answer. Thus, write (3x -- 1)(x -- 23). 3x times x is 3x^2, 3x times -23 is -69x, -1 times x is -x and -1 times -23 is 23. Thus, (3x^2 - 69x - x + 23) equals (3x^2 - 70x + 23) and is correct.
Swap the signs in the parentheses, if the parentheses have two different signs and the answer is still incorrect. If the signs are the same or the answer is still incorrect after switching signs, the trinomial is a prime trinomial and cannot be factored. The example trinomial contains two prime numbers but is not a prime trinomial, because it factored.