In general there are a number of ways of factoring. The last-ditch, but always working, method is to set the quadratic equal to zero and use the quadratic equation. This gives two solutions, x = a and x = b. Then the quadratic factors as (x - a)(x - b). (I call this a "last-ditch" method because it is the least elegant of the factoring methods.)Originally Posted by pashah
a) This one just isn't going to factor nicely, so I'm going to use the quadratic formula to do this. The solutions to the quadratic, when set equal to zero are . Thus
Usually when we factor we factor over rational numbers, so I'm guessing there may be a typo here?
b) This also is ugly and can be done using the quadratic formula.
c) The common factor in both terms is , so
(Using the difference of two squares factorization.)
d) First factor out the common factor of 20:
We may factor the remaining quadratic by the "guess method." Since the coefficient of the x^2 term in is 1 we know that it factors as . All we need do is guess at a and b.
So we know that ab = 4 and a + b = -5. Thus a and b are some combination of from the first equation and we get a = -1, b = -4 by trial and error from the second equation. Thus:
. So we finally have: