How do you factor the expression #25x^2 - 35x - 30#?
First, we can easily see that each term has a factor of
Now we just need to factor
We could use the quadratic formula to find the roots of the expression, however let's see if we can find an integer solution without resorting to that.
We are looking for integers
From the first equation, we know that
From the third equation, we know that
Testing out which set of pairs fulfills the second equation lets us find a solution
Then substituting those back in gives us
But we mustn't forget the original