How do you know when to solve a quadratic equation with factoring?

Answer 1

Can someone please explain this to me?

Answer 2

If the coefficients are reasonably small, I will look for factors first.
e.g. 2x^2 - 11x - 6
You know the factors can only be (2x ....)(x ....) for the front
and for the back in can only be (.... +2)(... -3), (.... -2)(.... +3), (.... +6)(..... -1), (.... -6)(..... +1)
With a piece of scrap paper, a pencil and some common sense, or having done a few thousands of these, it can be seen to be (2x + 1)(x - 6)

A foolproof way is this:
recall that for ax^2 + bx + c = 0 , using the formula we have the expression √(b^2 - 4ac) called the discriminant.
Evaluate that. If the result is a perfect square, it WILL factor,
e.g. for our example , b^2 - 4ac = 121 - 4(2)(-6) = 169, and √169 = 13
So it will factor!

If you are on a test, and the question demands that you solve it by factoring, but you can't find the factors, do the following
1. find the answers by using the formula, remember that you are looking for the discriminant to be a perfect square.
2. In our case , x = (11 ± √169)/4 = (11 ± 13)/4 = 6 or -1/2

x = 6 ----> the factor (x-6)
x = -1/2 ----> (2x+1)

so there you have the (x-6)(2x+1)