How do you factor #15b^2 - 7b - 2#?
We have a quadratic expression in the form
To factor this, first find two numbers that multiply to give
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.
Notice now that we have a common factor of
Let's factor it out:
And we're done!
It still would have worked if we had chosen to split the terms in the opposite order. Let's check: