2-3-31
X
00:00
/
00:00
CC
To do this problem, we're going to factor by grouping.
So we're going to group the first two terms together and
pull out what they have in common.
And then we're going to group the second two terms and factor
out what they have in common.
Now we went from 4 terms to two terms.
These two terms have an X + 9 in common, leaving us an X ^2 - 4 X
squared -4 is difference of two squares X + 2 X -2.
So the zeros are what make each of those parentheses go to 0, so
a -9, a -2 and a 2.
The multiplicity is just the power that each of those
parentheses is to, so in this case they're all to one.
Hence they're all odd, which means the Y values on one side
are going to be the opposite of the Y values on the other.
If I have a two and I have a -2 and I have a -9 because it's a
third degree equation with the leading coefficient that's
positive.
I know that out it when X is going to Infinity, I'm going to
have a positive value at this two.
It came from this term right here.
Multiplicity was odd.
So if the Y values on one side are positive, the Y values on
the other are negative.
When we go to the next X intercept -2, it came from this
term.
Here it's an odd multiplicity.
So if the Y values on one side are negative, the Y values on
the other side have to be positive.
This last zero came from this term, Once again, an odd
multiplicity.
So if the Y values on one side are positive, the Y values on
the other are negative.
So that's what our graph would look like.
So our zeros are -9 negative, two and two.
Our multiplicities are one, one and one, and the Y values on one
side of the zero and the Y values on the other side have to
be opposite because the multiplicity is odd.