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Now, we're going to do out some factoring problems that
use the perfect square trinomial factoring, and I'm
just going to tell you what to look for to know that you
might want to try to use that factoring.
So I'll do out two different problems, number
14 and number 16.
So first, we have factor v squared plus 14v plus 49.
All right, that's a trinomial so we can go ahead and use
that normal trinomial factoring if we want to from
Sections 6.3 and 6.4 or we can look and identify that we
might want to try the perfect square trinomial factoring.
And the way you identify it is if you have three terms with
perfect squares on both ends, the v squared and the 49 are
both perfect squares, then you want to try perfect square
trinomial factoring.
The way you do that is very similar to the
difference of squares.
You take the roots of the ends, v and v, 7 and 7, and
you put them in place, and then you keep the sign that's
at the beginning.
So right there.
Whatever your middle sign is, keep it down here.
And you see if it works.
If it works, you're all set.
Basically, you've got to check the middle term, because we
already know that v and v are going to give us the v
squared, and 7 and 7 the 49, because we knew that there are
perfect squares at the beginning.
So we need to check the middle term.
Middle term, we'll get--
check middle--
7v plus 7v.
Yes, it works, so that means this is going to
be the right factoring.
It will give us v squared plus 14v plus 49, if we were to
multiply it back out.
So this is how you can know that you want to use the
perfect square trinomial factoring, and usually I just
look and see if I have perfect squares on the ends, I try it
and see if it works.
If it doesn't work, I go to the
normal trinomial factoring.
Let's try one more, 6.5, number 16.
And this is where you can see that this approach can be
handy because if I look at t squared plus 1/3t plus 136, I
don't want to try factoring that using the other methods
like trial and error or the grouping method.
That seems like it would be a bit cumbersome.
So I'm going to look and say, hey, that's a perfect square,
and that's a perfect square, so I'm just going to try the
perfect square trinomial approach and see if it works.
Square root is t, square root of 1/36 would be 1/6 because
1/6 times 1/6 will give me 1/36.
And then I'm going to keep the sign.
So plus 1/6 plus 1/6.
And one more thing you want to do when you factor them out
this for your final answer, because they're both exactly
the same, you want to show it like that.
So in that last one we did we should have shown
it like that too.
So now, I double check the middle term to see if I'm
getting the right middle, so I'm getting 1/6t plus 1/6t
equals 2/6t, which is reduced to 1/3t.
Yep, the middle works.
So that would be my final answer.
And on number 14, final answer would be v plus 7, whole thing
being squared.