# How do you factor completely: #2x^2 + 4x − 2#?

##### 1 Answer

Either:

or

#### Explanation:

The phrase "factor completely" is not unambiguous as one might think.

When we factor poynomials, we usually have some perticula set of numbers we are willing to use as coefficients. In early aalgebra classes, we usually restrict ourselves to integer coefficinents.

**Using Integers:**

(The only possibility to get

**Using Rational Numbers**

We can get the factors for the plolynomial

by solving the equation

Use either completing the square or the quadratic formula to get:

So the factors are:

We get:

# = 2(x+1-sqrt2))(x+1-sqrt2))# .