How Do I Factor Quadratic Equations?

Factoring is a method for separating quadratic equations into the product of linear equations. The standard form of a quadratic equation is


and we want to find the factors of c which also add to b.

This might sound a little intense, but trust me it’s not bad at all. Consider the quadratic


The first step is to write down the factors of 6, which are (and this is important)

(1, -1, 2, -2, 3, -3, 6, -6)

The factors of 6 that also add to 5 are 2 and 3 (both positive).

The next step is to write out the linear factors of the quadratic. In this case, (x+2) and (x+3). These factors are usually written as a product


You can check that the linear factors you’re using are correct by multiplying them, which should result in the original quadratic equation.

The final step is to set each of the linear factors to 0 and solve for x. In this case

x+2=0 and x+3=0


x=-2 and x=-3


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