Here, we are looking for an answer in the form:
x^{2} − 5x − 6 = (x ... )(x ... )
Note that the term we have at the beginning of the question is x^{2}, so we put x in each bracket. This gives us (x)(x) = x^{2}, which is what we need for that first term.
Now we need 2 numbers that multiply to give −6 and add to give −5. The possibilities are:
multiply to give | add to give | OK? | |
2 and −3 | 2 × −3 = −6 | 2 + −3 = −1 | No |
−2 and 3 | −2 × 3 = −6 | −2 + 3 = 1 | No |
6 and −1 | 6 × −1 = −6 | 6 + −1 = 5 | No |
−6 and 1 | −6 × 1 = −6 | −6 + 1 = −5 | OK |
So we have:
x^{2} − 5x − 6 = (x − 6)(x + 1)
This method of factoring can be tedious because we may need to try several combinations before we hit on the correct numbers (and letters).
After some practice, though, you can spot the most likely combination of letters and numbers. I've shown all the possibilities in the table to give you an idea of what can be involved.
Easy to understand math videos:
MathTutorDVD.com