00:01
We now determine the possible roots of the polynomial function f of x according to the rational root theorem.
00:07
So as per the rational root theorem to determine the possible roots, we consider the coefficient of the highest term of this polynomial.
00:16
The highest term of this polynomial is x cube and its coefficient is 4.
00:21
So we see this as the leading coefficient.
00:28
We consider the factors of this leading coefficient.
00:32
And we also consider the constant term in this polynomial function.
00:37
We also write down its factors.
00:40
So first, let's write the factors of the leading coefficient.
00:43
The leading coefficient is 4 and its factors, we can write down this as plus r minus 1, plus r minus 2, and then plus r minus 4.
00:53
So these are the factors of 4, which is the leading coefficient of this polymer function.
00:59
Let's say we can call this as k.
01:02
Factors we consider this as k.
01:04
And now let's consider the constant term, which is 10.
01:08
We also write down its factors.
01:11
So its factor is going to be plus r minus 1, plus r minus 2, plus r minus 5, and then plus r minus 10.
01:19
It's called these factors as h.
01:23
So we got the factors of the leading coefficient as well as of the constant term.
01:29
Now according to the rational root theorem, the the possible roots of this polynomial function, possible roots, is given by this fraction, that is h by k.
01:46
That is, we have to consider all the fact, all the combinations of this h by k.
01:53
And then those are the possible roots of the polymer function.
01:57
So if we consider the one of the h that is a plus r minus 1, so we divide plus r minus 1 divided by this plus r minus 1 and that will give plus r minus 1.
02:12
So i'm going to write down this as plus r minus 1.
02:17
And then if i consider this plus r minus 1 divided by plus r minus 1, so it's going to give plus r minus 1 divided by 2.
02:27
And then now i do the other factor.
02:32
It is plus r minus 1 divided by plus r minus 4.
02:36
That will be plus r minus 1 divided by 4.
02:39
So we have we have calculated for the factor plus r minus 1 and making a combination with all the factors in k.
02:49
So we got this one.
02:51
Now let's consider the next factor in h that is plus r minus 2.
02:55
And then we have to divide this h by all the three factors in k...