00:01
All right.
00:01
So to begin with, we are going to factor this trinomial.
00:05
Then we'll use zero product property to solve from there.
00:08
So i'm going to begin by figuring out the possibilities.
00:15
So i'm going to multiply the first and the last terms.
00:18
And that will make 56f squared.
00:25
And 56f squared can either be made with 1f times 56f, 2f times 28f.
00:36
3 cannot make it 4 times 14, 5 cannot make it, 6 cannot make it, 7 can 7f times 8f, or the reverse of any of these.
00:50
So these are the pairs that we can use.
00:53
And we want them to multiply to a positive, which means that they're the same sign.
01:00
Together, these are going to be the products that you see here and here.
01:05
And we want those two products to combine to our middle term, which is negative 15.
01:09
So which of these combines to negative 15? 57, 30, 18, 15.
01:20
So this is the pairing that we need.
01:23
7f and 8f.
01:27
Now if we look at our terms here, we can get a 7 from here, but not from here.
01:33
And so i want f and 7 to be the first and last terms in these two different binomials.
01:42
That means to make this, i still need 4f.
01:45
So 4f will go here...