00:01
Okay, well, let's consider a general polynomial of degree less than or equal to three.
00:08
Such a polynomial is going to have the form a x cubed plus b x squared plus cx plus d.
00:18
Now what do we want? we want that f of one, which is just a plus b, plus c must be equal to or plus d must be equal to what must be equal to f prime of negative one but f prime of x is what f prime of x is 3 a x squared plus 2 bx plus c so f prime of negative 1 is going to be 3a plus okay plus actually minus to b plus c this is just f prime of negative one so by using these two equations what do we find well we find that we find that okay we can get rid of this one and this one in this equation so we find two a plus oh sorry minus 3b minus 3b equals 0 okay oh and sorry i forgot the minus 3b minus d equals 0 so for example we can set we can set for to find the first polynomial p of x we can set a equals 0 b equals 1 and d equals negative 3 so we find the first polynomial which is x squared x squared b can be x squared c can be whatever we want so for example we can set it equal to 0 and this is going to be equal to negative 3.
02:56
So x squared negative 3.
02:59
This is the first one.
03:00
Now, in order to find the second one, we can set, for example, b equals 0.
03:11
And for b equals 0 and a equals 1, we have the equals 2.
03:20
So the second polynomial q of x is going to be what? the second polynomial q of x is going to be x cubed.
03:33
C can be again whatever we want.
03:36
So we can adjust set it equal to zero.
03:41
And d is going to be equal to two...