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(male narrator) In this video,
we will begin looking at factoring trinomials.
A trinomial is often in the form of a quadratic,
which means ax squared, plus bx, plus c--
where a, b, and c will be numbers,
and x is what the variable is in our expression.
We often will factor these using what is called the AC method,
which gets its name, because we're going to find
a special pair of numbers that multiply to a times c
and add to the middle number, b.
As we do, we will make a cross, putting the AC on top--
showing that we're multiplying to the AC--
and the b on the bottom--
showing that's what we're adding to.
We're looking for the two numbers--
the one unique pair of numbers that make this work.
These will help us factor, because using FOIL,
these numbers will come from the O and the I--
or the outside and inside.
Let's take a look at an example
where we can see this worked out.
In this problem, in order to factor it,
we set up our cross
and putting what we want to multiply to on the top,
which is AC: 3 times 10 is 30.
And we want to add to the bottom...
the middle number, 11.
There are several ways to multiply to 30--
for example, 2 times 15.
However, you notice those numbers
will not add to the 11 we want.
Another way to multiply to 30 would be 3 times 10.
However, those also do not add to the 11 we are looking for.
Finally, we could consider 5 times 6.
Notice, 5 times 6 is 30, and 5 plus 6 is 11.
This is the pair of numbers we will use
to get the 11x in the middle.
We will use 5x and 6x.
With that in mind, we will begin to make our factors,
keeping in mind FOIL.
Trinomials will factor to two binomials,
where the first term comes
from multiplying the first times the first.
To get 3x squared, the only way to do so, would be 3x times x.
To figure out what goes in the last two positions,
we consider the outside and inside numbers.
In other words, 3x is multiplied by something,
and x is multiplied by something.
And the answers from those two problems are 5x and 6x.
I always start with the larger number--the 3x:
3x times something; 3x times what is 5x.
Well, we really can't do that,
so maybe we want the other number.
Can we multiply 3x by something to get 6x:
3x times +2 is 6x,
and that gives us the 6x we want.
In the center, then,
we will attempt to get the other number--the 5x:
x times something will be 5x;
x times +5 is 5x, and that completes our problem:
3x plus 5, times x, plus 2, when multiplied out,
are the factors used to get 3x squared, plus 11x, plus 10.
In the next video,
we will take a look at doing one more example.