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| Factoring in Algebra |
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 ax2 + 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:
x2 + 2x + 1
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:
(x + 1)(x + 1)
Example 2:
x2 + 7x + 12
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:
(x + 7)(x + 4).