The general form for quadratic equations is:

Ax^2 + Bx + C = 0

If A ≠ 1, then use the quadratic formula. It's usually the slowest way, but it always works, unlike other methods. The only downside to it is having to use it during a test, since it takes more time. A few other methods that you can use for A ≠ 1 are listed at the bottom of this page.

If A=1, you have x^2 + Bx + C = 0, and the following procedure always works.

The general form of the factors in this case will look like:

(x + D)*(x + E)

The product of D and E is C (D*E = C), and the sum of D and E is B (D+E = B).

In order to find help us find D and E, it's useful to figure out whether they are positive or negative first. We find out by using the following procedure which I call the "Sign Method."

Scenario #1: If C is negative

Step 1:

We know that either D is positive and E is negative, or vice versa (E is negative and D is positive).

Step 2:

If B is positive, we know that the factor of C with the larger absolute value will be positive and the other factor of C will be negative.

If B is negative, we know that the factor of C with the larger absolute value will be negative and the other factor of C will be positive.

Scenario #2: If C is positive

Step 1:

We know that D and E are both the same sign (either both positive or both negative).

Step 2:

If B is positive, C and D are both positive. If B is negative, C and D are both negative.

Once you've figured out the signs (positive or negative) for D and E, then all that's left is to find two factors of C that add up to equal B. In other words, if D*E = C and D+E = B then you're answer is right.

In addition to the quadratic formula, you should know that there is a second shortcut for factoring quadratics when A ≠ 1 that's called the “Modified ABC Method" or "Box Method" which uses factoring by grouping.

There is also a third convenient shortcut for solving quadratics when A ≠ 1 called the “Diamond Method.”

Lastly, a fourth shortcut for factoring quadratics has recently been found in 2019 which I call the "Ancient Method."