Southbay Math Tutor: Factoring Trinomials I (Algebra)

Uploaded by SouthbayMathTutor on 20.06.2010

We're going to Factor a trinomial with a method that's been called:
The box, the diamond, bottoms up.
Doesn't matter what you call it
just as long as you get the answer right(chuckles).
So we're gonna start off by making a large 'X'...
So we look for factors of 30.
So we go '6 x 5'...'10 x 3'... '15 x 2'...'30 x 1'
I think that's about it there, right?
So these all multiply together to equal 30.
But which one of those also adds up to be -13x?
So we go through each of them one at a time.
30x x 1x = 30x squared, but 30 + 1 = 31 so it can't be that one.
15x x 2x = 30x squared. Let's see, -15x + 2x = -13x...Thought that
might be it. Close but no cigar.
Let's see...10 x 3 = 30... Oh look, if we put -10x and -3x...
Well -10x x -3x = 30 x squared and -10x + -3x = -13x
So that one's a winner. We don't even need to look
at the last one here. But just for the heck of it
we'll look at it, just to be sure. 6 x 5 = 30 but
6 + 5 = 11... -6 + -5 = -11 So that one doesn't work.
So definitely that's the combination we're looking for
-10 x -3 = 30 , -10 + -3 = -13.
Now we're going to make our binomial...
So you take the lead coefficient of the first term of your binomial(5),
and you bring the 5 and you place it underneath the 10.
And you have 10 divided by 5.
Then you bring the 5 over here. And you have 3 divided by 5.
10 divided by 5 is 2, so we write: (x-2)
and 3 divided by 5 we will leave as a fraction: (x-3/5)
Now we look at the denominator in the second term of each binomial.
In this case we have 2/1,right? 2 over 1 is the same as 2/1.
Bring the '1' (denominator) in front here.
You do the same thing with the second binomial.
The 5 is in the denominator so you bring it up front.
So you have 5x - 3. The 5 goes away.
And there's your answer: (x-2)(5x-3)
Checking your answer: 5x times x = 5x squared
-3x + 10x = -13x and -2 x -3 = 6.
Add it up and you have 5x squared -13x + 6
So there's your answer.