00:01
Hello.
00:01
So in a polynomial, we have to have that the variable has to be raised to non -negative integer powers, basically.
00:12
So it's hard to tell exactly what the given functions are.
00:17
But here we have a few examples to see if we have polynomials or not.
00:22
So in the first example, here we have f of x, which is going to be equal to, well, x to be eighth, plus 8x to the negative 6th minus 2.
00:28
While this negative 6, right, we cannot have a negative exponent.
00:32
So therefore, no, that is not going to be a polynomial.
00:36
Likewise here, for the second one, what we have 8 times the square root of x minus 9x to the 5th.
00:42
Or just minus 9x to the 5th, that's fine for a polynomial.
00:45
But again, the square root of x is the same thing as x to the 1 .5 power.
00:49
So we write this as 8 times x to the 1⁄2 power and then minus 9x of the 5th.
00:55
That's the same thing.
00:56
But then again, we now have a fractional exponent.
00:58
For the square root of x...