Factor and Multiply to Check

Date: 5/21/96 at 16:0:14
From: Beverly Jenkins
Subject: Factoring

Dr. Math,

I am in Algebra 1.  Here's are the directions:

Factor.  Check by multiplying the factors.  If the polynomial is not 
factorable, write "prime."  

The first problem is x to the second power plus 6x plus 5.  

Help if you can!

Date: 7/2/96 at 16:11:36
From: Doctor Leigh
Subject: Re: Factoring

Beverly,

Your teacher probably wants you to see if you can use one of a couple 
of methods to factor an equation.

One possible method for factoring equations is done by finding a 
common factor and then factoring it out.  Since there are no common 
factors in x^2 + 6x + 5, we need to try something else.

Another possible method is called the difference of two perfect 
squares.  If an equation consists of two perfect squares with a 
subtraction sign between them, the equation can be factored using this 
method.  However, since this equation is not the difference of two 
perfect squares we should try another way.

A third possible solution is using reverse FOIL.  This is used if you 
have an x squared term along with an x term and then a constant (no 
x).  You try to find two numbers that, when added, add up to the 
middle number, and when multiplied are the constant.  Are there any 
such numbers that add up to be 6 and multiply to be five?

Yes!  One times five is five, and one plus five is six.  So, our 
factors are (x+1)(x+5).

Multiply these out to check.

Thanks for your question. I hope I was able to help.

-Dr. Leigh Ann    The Math Forum
 Check out our Web site:  http://mathforum.org/dr.math/