00:01
The graph of the polynomial p of x is given and the degree of this polynomial is 3.
00:05
So first we write the polynomial in factor form.
00:09
So p of x this equals for that we consider the zeros of the polynomial.
00:15
This one has zeros at negative 1 and 5 and also at 6.
00:22
So we write this polynomial.
00:24
We put the constant a first and then multiply this with the first factor using the first zero.
00:30
That is x minus the 0 is negative 1.
00:34
So it will be x minus 1.
00:36
And then the next to 0 is 5.
00:41
So we write x minus 5.
00:43
And then the next to 0 is 6.
00:45
So we write x minus 6.
00:47
Now we can simplify this x minus 1 that is x plus 1.
00:53
So this is the polynomial in factor form.
00:56
However, we should determine this constant a.
00:59
And for that, we use this information, that is the y intercept of this polynomial is 30, which means at x equals 0, p of x, that is p of 0 equals 30.
01:14
So i'm going to replace all x in this polynomial function by 0.
01:18
That means we get p of 0.
01:21
This equals 8 times.
01:23
Replace x by 0 that will be 0 plus 1 and 0 minus 5 0 minus 6 now p of 0 is 30 so here we can replace this p of 0 by 30 so let's solve this equation for a this equals a times 0 plus 1 is 1 0 minus 5 is negative 5 0 minus 6 is negative 6 so this gives 30 this equals 30 this equals 1...