Proton basic serial interrupt in 8051 numbers. [Voiceover] So we're asked, Is the expression x minus three, is this a factor of this fourth degree polynomial? And you could solve this by doing algebraic long division by taking all of this business and dividing it by x minus three and figuring out if you have a remainder. If you do end up with a remainder then this is not a factor of this. But if you don't have a remainder then that means that this divides fully into this right over here without a remainder which means it is a factor.

So if the remainder is equal to zero, the remainder is equal to zero, if and only if, it's a factor. Imagenomic portraiture 2.3.08 plugin for photoshop. It is a factor. And we know a very fast way of calculating the remainder of when you take some polynomial and you divide it by a first degree expression like this. I guess you could say when you divide it by a first degree polynomial like this. The polynomial remainder theorem, the polynomial remainder theorem tells us that if we take some polynomial, p of x and we were to divide it by some x minus a then the remainder is just going to be equal to our polynomial evaluated at our polynomial evaluated at a. So let's just see what's a in this case.

Well in this case our a is positive three. So let's just evaluate our polynomial at x equals 3, if what we get is equal to zero that means our remainder is zero and that means that x minus three is a factor. If we get some other remainder that means well we have a non-zero remainder and this isn't a factor, so let's try it out. So, we're gonna have, so I'm just gonna do it all in magenta. It might be a little computationally intensive. So it's going to be two times three to the fourth power, three to the fourth, three to (mumbles), that's 81.