# How do you factor completely: #3x^2 + 12x + 7#?

##### 1 Answer

It depends on what kinds of numbers we are using.

#### Explanation:

Using integers (or rational numbers) this quadratic cannot be factored any further. It is already factored completely.

(The only possibilities are

If we are using Real numbers or Complex numbers, we can factor the quadratic by finding its zeros.

Solve

# = (-12 +- sqrt (144-84))/6 = (-12 +- sqrt 60)/6 = (-12 +- 2sqrt 15)/6#

# = -2 +- sqrt 15/3#

The zeros are:

The factors are:

# = (x + 2 - sqrt 15/3))(x + 2 + sqrt 15/3))#