# How to Factor

1. Jan 8, 2010

### Jordash

1. The problem statement, all variables and given/known data

How would you solve this problem:

x^2 - 5x >= 0

2. Relevant equations

3. The attempt at a solution

I think it might be something to do with the Quadratic Formula?

2. Jan 8, 2010

### Staff: Mentor

Look at it as two problems: x^2 - 5x = 0 and x^2 - 5x > 0. For the first problem, the simplest way is to factor the quadratic expression, which will give you two solutions. These two numbers divide the number line into three regions. Pick one value in each region and determine whether it satisfies the inequality. If one number in a region satisfies the inequality, every number in the region will satisfy it.

3. Jan 8, 2010

### HallsofIvy

It should be fairly clear that $x^2- 5x= x(x- 5)$. Once you have done that you can use the facts that "positive times positive is positive" and "negative times negative is positive".

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