Associated Topics || Dr. Math Home || Search Dr. Math

### The Steps of Factoring

```
Date: 08/08/98 at 10:53:10
From: Brandie
Subject: Factoring problems

My question concerns the following problems:

Given y^2 - 14y + 24

a. write factors of the first term: (______)(_______)

b. signs are ________________ because the sign of last term of the
trinominal is positive and the sign of the middle term is
_________________________: (________________)(________________)

c. find factors of 24 whose sum is -14: _____________and___________

d. complete:(___________________)(______________________)

I am also have trouble factoring:

a^2 + 25a + 24 = (a+1)(a+_______)

y^2 - 12y + 27 = (a-3)(a-_______)

Please also can you tell me where to go and look for more help on
factoring in Algebra I.
```

```
Date: 08/14/98 at 13:24:01
From: Doctor Margaret
Subject: Re: factoring problems

Hi Brandie,

Thanks for writing to Dr. Math. It looks as if you are just starting to
learn to factor. This is a very nice way of giving a factoring problem
because it lists all the things you have to do. It might help for you
to remember that the factors of a number are two numbers that when
multiplied together give you the number. For example, the factors of
12 are:

1 * 12
2 * 6
3 * 4

In factoring a trinomial we want to get the numbers that, when
multiplied together using the FOIL method, give us back the trinomial.
There is a method for this. First, we find out the factors of the
first term in the trinomial.

The factors of y^2 (that's how we write y squared) are y * y.

There are two signs in the trinomial between the three terms. The sign
on the last term gives us a clue about both of the signs within the
parentheses. It would be good if you could memorize:

- If the sign on the last term is positive, both signs in the
parentheses are the same.

- If the sign on the last term is negative, then the signs in the
parentheses are different.

- If the signs are the same, the first sign will tell you if they are
positive or negative.

In your first example, we know that both parentheses will contain
negative signs.

Now let's look at the factors of 24 that will add up to -14. Remember
that factors are numbers which in this case multiply together to get 24
and add to get -14.  The factors of 24 are:

1 * 24
2 * 12
3 * 8
4 * 6

If we make 2 * 12 into -2 * -12 these numbers multiply to 24 and add
to -14:

(-2)*(-12) = 24
(-2)+(-12) = -14

y^2 -14y + 24 = (y -2)(y - 12)

We know that this is true because, using FOIL, we get:

First: y * y = y^2
Outer: -12 * y = -12y
Inner: -2 * y = -2y
Last: (-2)*(-12) = 24

So: y^2 -12y -2y + 24 = y^2 - 14y + 24, which is what we started with.

Try to do the next two problems by yourself. It would be a good idea
to practice a lot. It does get easier, and you will be using it for a
long time, so you have to get good at it. There are also some problems
in our Dr. Math FAQ:

http://mathforum.org/dr.math/faq/faq.learn.factor.html

Feel free to write back if you are still having trouble, and try to
include any work you've done so we can see exactly where you are stuck.

- Doctor Margaret, The Math Forum
Check out our web site! http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Factoring Expressions

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search