00:01
So we can use the factor by grouping method to factor this problem and find the zeros.
00:07
And so if we look at the first two terms here, if we factor out an x cubed, what we're left with is is x minus 2.
00:15
And so now if we look at our next two terms, we want one of the terms to be x minus 2.
00:20
So if we factor out a negative 8, well, what we're left with is is x minus 2.
00:26
So we have x cubed minus 8 times x minus 2.
00:33
And so now we have we have x cubed has to equal 8.
00:38
And so x has to equal 2 to find our zeros.
00:42
So if we take the cube root of 8, well this this has to be this x cubed has to be 8.
00:50
So now we we say x is the cube root of 8 and so this is 2.
00:58
We have x is equal to two for both so we have we have that x is equal to two is our only zero and this has a multiplicity of two so this will only this will only touch the x axis and so now let's look at our boundaries here well when x tends to positive infinity we have we have positive infinity times positive infinity so our our polynomial will tend to positive infinity and as x tends to negative infinity well our polynomial will tend to, let's see here, we have negative infinity times negative infinity, so this will also be positive...