00:02
So remember the first thing we want to do if we want to sketch a polynomial is find the intercepts as well as there are multiplicities.
00:11
It's fine the x intercept as well as the multiplicity.
00:15
So we have an x intercept at x is equal to positive 1 with a multiplicity of 2.
00:22
And so this means we will touch the x axis.
00:25
And we have an x intercept at x is equal to negative 2, which has a multiplicity of 3.
00:33
And so the multiplicity of three means that the multiplicity of three means we will cross the x -axis since this is a odd multiplicity so let's look at our end behavior here well we if we have x is approaching positive infinity well we have positive infinity squared so we'd have positive infinity squared which is positive infinity and we'd have a positive infinity cubed so this this polynomial approaches positive infinity approaches positive infinity.
01:08
And so now when x is approaching negative infinity, well, our polynomial will approach negative infinity because negative infinity squared is positive and negative infinity cubed is negative.
01:21
So we have a positive times negative, which gives us negative infinity.
01:25
So now we can sketch this polynomial.
01:28
So this is our y -axis and this is our x -axis here...