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title: Factoring in Algebra
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## Factoring in Algebra

Factoring is how you take a quadratic in standard form and put it in factored form. The standard form for a quadratic is normally shown as ax<sup>2</sup> + bx + c where a and b are coefficients and c is a constant. Factored form is normally shown as (x - d)(x - t) where d and t are both coefficients.

## Factoring in Your Head

This method of factoring usually works best when a = 1. To do this when a = 1 you look at what two numbers add to equal b while also multiplying to c. Those two numbers will then be equal to d and t.

#### Example 1:<br>
x<sup>2</sup> + 2x + 1<br>
Here you have to look for two numbers that multiply to 1 and add to 2. Those two numbers are 1 and 1. Then you put those numbers into the factored form like this:<br>
(x + 1)(x + 1)

#### Example 2:<br>
x<sup>2</sup> + 7x + 12<br>
Here you have to look for two numbers that multiply to 12 and add to 7. Those two numbers are 3 and 4. Then you put those numbers into the factored form like this:<br>
(x + 7)(x + 4).