Determine the degree of each polynomial. − x 4 + 2 x 3 − 5 x 5 − 8 x -x^4+2x^3-5x^5-8x

Folks, so let's keep going with our next practice problem. We're going to determine the degree of the polynomial itself, and here we have a little bit of a longer one. We've got negative x to the fourth power plus two x cubed minus five x to the fifth power minus eight x. Again, the degree of the polynomial is the highest out of all of the terms inside that polynomial. We know how to do that, so we're just going to go ahead and figure out the degree of each term and then just pick the largest one. Alright, so if I look at negative x to the fourth power, what's the degree of that? There's only a single variable in front of with all of these, single terms that are here. It's only just x, so we don't have to sum any exponents of multiple variables or x to the fourth power, the degree is just four. What about two x to the third power? Well, again, coefficients don't really do anything to the degree of the term, so we just look at the exponent. The exponent is three, therefore the degree is three. Again, that only works just because we have one variable here of x. Here, what about this? We've got five x to the fifth power, you look at the exponent and the degree is five. It's not because the coefficient is five, it's because of the exponent of five. The degree is five, and then over here we have 8x, so minus 8x. Now, again, remember we don't see exponents just because there's kind of like an invisible one that we've seen there before, So, the degree of this term is one. Alright, so now what we do is we just look at the highest out of all of the terms in this polynomial and that tells us what the degree of the polynomial is. Alright, so the degree of the polynomial, this is the largest one that we see out of all the terms, and that's going to be this one, the five. Alright? So, that's the degree of our polynomial. They don't necessarily have to be in sort of descending or decreasing order of exponents. Many of the times you'll see expressions like this where you can see exponents that are all over the place. Alright? So, again, this is why it's really, really important to look through your variables very carefully in terms because many students will just make the mistake of looking at the first term and thinking, okay, this is just a degree of four here. You have to look at all of them before you can make the determination. Alright? Thanks for watching. Let me know if you have any questions. Let's move on.