Factoring a Quadratic Equation

Date: 05/13/98 at 16:26:27
From: Alexander Yung
Subject: Algebra

Factor y^2 + 2y - 35 = 0.

Date: 05/20/98 at 10:09:52
From: Doctor Alice
Subject: Re: Algebra

Hello, Alexander!

Well, your problem is a quadratic equation. And you want to solve it 
by factoring a quadratic trinomial into a product of two binomials.

Look at the y^2 first. It breaks down into y times y:

   (y      )(y      ) = 0

Now look at the 35. List its pairs of factors. Factors are numbers 
that when multiplied give us our product. So what two numbers can you 
think of that when multiplied give you 35?

What about 35 and 1? Or 7 and 5?

Now, which of those pairs could give us a 2 (coefficient of the linear 
term, that means the number in front of the y^1 term) if we played our 
signs right?

Of course: 7 and 5.

So we have: 

   (y     7)(y     5) = 0

Now for the signs -- sometimes the hardest part of factoring. Look at 
the sign of the constant term -35. When is a product of two numbers 
negative?

When one of them is + and one of them is -. 

Now we have either:

   (y - 7)(y + 5) = 0  or  (y + 7)(y - 5) = 0

Which one? Use the FOIL method to multiply the outer and inner 
products, because we need to get +2y. The left equation expands to 
contain 5y - 7y, and the right choice has -5y + 7y. We want the right 
one.

So the factorization of your quadratic equation is:

   (y + 7)(y - 5) = 0

To finish it off, set each factor equal to 0 and solve.

I hope I have helped.

Write back if you are still confused.

-Doctor Alice, The Math Forum
Check out our web site! http://mathforum.org/dr.math/