# How do you factor #15b^2 - 7b - 2#?

##### 1 Answer

#### Answer:

#### Explanation:

We have a quadratic expression in the form

To factor this, first find two numbers that multiply to give

For

Maybe you can see by inspection that these two numbers are:

How did I see that? Look at the factors of

Now try adding or subtracting them to get

Remember that one of them (and ONLY one of them) must be negative so that we get

Now it's much easier to see that

So why did we do this? Our original expression was

Let's now split the middle term using the numbers we just found.

Now factor

Notice now that we have a common factor of

Let's factor it out:

And we're done!

NOTE:

It still would have worked if we had chosen to split the terms in the opposite order. Let's check: