Expert: Paul Klarreich - 3/11/2008

Question
Hi my name is Haley and I am confused on how to factor this problem into two binomials: 2x squared + 15x + 7. Please help me. Thank you.

Answer
Questioner:  Haley
Private: no
Question:  
Hi my name is Haley and I am confused on how to factor this problem into two binomials: 2x squared + 15x + 7. Please help me. Thank you.
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Hi, Haley,

[Note: this question belongs in ALGEBRA, not advanced math.]

2x^2 + 15x + 7 factors to (2x + 1)(x + 7)

But you probably want to know the process, I think.

1. There is no common factor.  That is always always always always always the first step. No exceptions.

2. 2x^2 is factored as 2x times x.  Now make a framework.

2x^2 + 15x + 7 = (2x    )(x    )


3. 7 can only be factored 7 times 1. List all the ways to fill in the framework:

2x^2 + 15x + 7 = (2x + 7)(x + 1)  [Trial A]
2x^2 + 15x + 7 = (2x + 1)(x + 7)  [Trial B]

Now compute the 'cross-products'.  Never mind doing 2x * x or 1 * 7 -- those will be right.  Just try:

A. 2x times 1 and 7 times x gives 2x + 7x = 9x.  No good.
B. 2x times 7 and 1 times x gives 14x + 1x = 15x.  Real good.

B is the right one.

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Comment: In many cases, there will be many more than 2 possibilities to try.  This one was pretty simple.  You will learn some 'tricks' to cut down on the trials. (Ask your teacher - she knows them all.)