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Introduction to Polynomials - Problem 1

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

Polynomials; so in this particular problem we are just going to deal a little bit with some language and some specifics by polynomials. So up here I have g(x) which is a polynomial and the first thing we are asked is to state the degree of each term.

So basically that’s just the power on x of these term. So just looking at here we have a degree 2 degree 1, x is just x to the first. Here we have x² and x so we can actually combine those. Remember when we multiply our bases we can add our exponents so this actually can be combined to be x³ which is the same thing as a third degree.

Here is a constant term, so there is no x, x to 0 so the degree on this term is a 0 and lastly x² is a degree here is 2, okay easy enough. Let us take the degree of g(x) the entire polynomial. So for this one we just look at the degree of the largest term. So for that one we have a 2, 1, 3, 0 and 2, our largest degree is 3. So the degree of the whole polynomial is 3.

Common mistake is to wanting to add up all these numbers together. Don’t just look at the term of the highest power.

Then it says write the degree in descending order, so descending order is when we write it from highest degree to lowest degree, so looking at it our third degree is going to go first. So we'll just have g(x) is equal to 8x³.

Now we have a second degree we have a second degree 7x² and 4x² we can combine like terms so this becomes 11x² then we go to our first degree 5x and lastly our constant term minus 8. So just looking at our polynomial talking a little bit about degrees and descending order how we organize everything.

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