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

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

(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/
```
Associated Topics:
Middle School Factoring Expressions

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