Trinomials



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Trinomial - Yet another impressive math word.  The meaning is fairly simple, the expression has three terms, one of which is usually the variable squared (but not always).

In the image above, there are two tri - nomials.  They are simply expressions with three terms.  By the way, I seldom (never) see it spelled with a hyphen like that.  I just did to point out the tri meaning 3, like tricycle is a 3 wheeled bike.

Question #14 in the aMAZEing Math Maze.

Congratulations on making it this far - very impressive.  O'k, here's the question.

Which one of these trinomials can not be factored using integers?

A) x2 + 3x - 10

B) x2 + x -12

C) x2 + 2x - 1

D) x2 + 2x - 3

Choose one (remember, this is the term that can not be factored using integers.

A)  B)  C)  D)   

 Trinomials - As if we needed additional explanation, a little more about the word.

Of course this question was about more than knowing the definition of a math term.  The trick with this one is figuring out which of the expressions can be factored.  I'll go into a bit more detail on that in a minute.  First I'm supposed to create an outbound link.  I chose Wyzant as they offer tutors (for a price).  In addition they also have printed resources - in this case, I chose what addressed the problem we're working.

Factoring quadratics

We are looking for two numbers that multiply together to give the third term in the expression.  These two numbers have to add together to give the coefficient of the middle term.  In this case, we are assuming that the squared term has a coefficient of one.

Still a bit confused.  Let's look at a general example.  I'm going to use the letters a, b, and c as coefficients and x as my variable.  So, in the expression-

ax2 + bx + c

We start by looking at the numbers that can multiply together to equal c.  The factors of c - if you will.

Now, see if those two numbers add together to equal b.  If they do - we can factor this puppy.  Assuming that a = 1.

A bit too abstract?  Let's try it with a real expression.

x2 + 5x + 4

First note that the coefficient of the first term is 1, if it wasn't, we could still do this - it would just be a little more work.

So, what are the factors of 4?  The third term in the expression is 4 and the pairs of numbers that multiply together to get 4 are

1 x 4

2 x 2

4 x 1

Now, looking at the first pair 1x4 does those two factors add up to be the coefficient of the middle term?  The middle term is 5x and the coefficient is 5.  They do!  so

x2 + 5x + 4

Could be factored to equal (x + 4)(x + 1) - mulitply those out and you'll get back to the original equation.

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