How do you factor (x^2-2x-4)?


Quick Answer

The expression (x^2 - 2x - 4) factors as (x + 1 - sqrt(5))*(x + 1 + sqrt(5)), where sqrt(5) is the square root of 5. This quadratic polynomial is factored by completing the square, a method in which a particular number is both added to and subtracted from the polynomial in order to factor the polynomial.

Continue Reading

Full Answer

To complete the square, begin by writing the polynomial as x^2 - 2x = 4. Note that the left-hand side can be factored into (x - 1)^2 if 1 is added to the expression. The number 1 must also be added to the right-hand side so the polynomial remains the same: x^2 - 2x + 1 = 4 + 1. Now the polynomial simplifies to (x - 1)^2 = 5. Solve this expression for the value of x by taking the square root of both sides and adding 1 to both sides. The right-hand side can be either the positive or the negative square root of 5; thus, there are two possible solution values for x: x = 1 + sqrt(5) or x = 1 - sqrt(5). A quadratic polynomial that factors can always be written as (x + A)*(x + B), where A and B are the two values of x at which the polynomial is equal to zero. In this case, the polynomial x^2 - 2x - 4 factors as (x + 1 + sqrt(5))*(x + 1 - sqrt(5)).

Learn more about Algebra

Related Questions