00:01
The trick to this problem, or at least the first part, we have this 2x cubed plus 3x squared minus 8x plus 3 is the possible rational roots.
00:14
I'll just write like this, p, r, r, is that you're looking at all the factors of the leading coefficient and all the factors of the constant.
00:24
And what i typically do is i just write out positive or negative the factors of the constant.
00:30
And what i'm doing is i'm taking the constant and dividing by one, which is a factor of the leading coefficient.
00:37
But those aren't the only correct answers because i can do the factors of the constant divided by other factors.
00:44
So one half.
00:46
And then plus or minus three halves.
00:49
And these are the only possible rational roots of this problem.
00:53
That's part a, i believe.
00:55
And then in part b, they go ahead and tell you that one of the ones at work, is negative 3.
01:02
So what i typically do is synthetic division.
01:05
Now, different teachers have different ways of doing synthetic.
01:09
This is just how mine looks.
01:11
And notice all the coefficients are copied down.
01:15
And what you do is you add down, so just this is two, and then you multiply by the number i put in the box.
01:22
So two times negative 3 is negative 6.
01:25
Again, add down, 3 plus negative 6 is negative 3 and multiply by what's in the box.
01:32
Add down and when you multiply by what's in the box, you know it works if you get a remainder of zero.
01:40
And so check that i guess all of this work is what you need for letter b.
01:45
So what does that mean? why do we do that? is that, so x equals negative 3 is a root and x plus 3 is a factor...