Writing a trinomial as the square of a binomial

This seems like a very complicated word, but if you break it down it'll start to make sense, especially when we start to see examples of polynomials. The first part of this word, lemme underline it, we have poly. This comes from Greek, for many.

Writing a trinomial as the square of a binomial

Adding and subtracting polynomials Video transcript In this video I want to introduce you to the idea of a polynomial. It might sound like a really fancy word, but really all it is is an expression that has a bunch of variable or constant terms in them that are raised to non-zero exponents.

So that also probably sounds complicated. So let me show you an example. If I were to give you x squared plus 1, this is a polynomial.

writing a trinomial as the square of a binomial

This is, in fact, a binomial because it has two terms. The term polynomial is more general. It's essentially saying you have many terms. Poly tends to mean many.

Fractional Exponents

This is a binomial. If I were to say 4x to the third minus 2 squared plus 7. This is a trinomial. I have three terms here. Let me give you just a more concrete sense of what is and is not a polynomial.

That doesn't mean that you won't ever see it while you're doing algebra or mathematics. But we just wouldn't call this a polynomial because it has a negative and a fractional exponent in it. Or if I were to give you the expression y times the square root of y minus y squared.

So all of the exponents on our variables are going to have to be non-negatives. Once again, neither of these are polynomials. Now, when we're dealing with polynomials, we're going to have some terminology. And you may or may not already be familiar with it, so I'll expose it to you right now.

The first terminology is the degree of the polynomial. And essentially, that's the highest exponent that we have in the polynomial. So for example, that polynomial right there is a third degree polynomial.

Now why is that? No need to keep writing it. Why is that a third degree polynomial? Because the highest exponent that we have in there is the x to the third term.

So that's where we get it's a third degree polynomial. This right here is a second degree polynomial. And this is the second degree term. Now a couple of other terminologies, or words, that we need to know regarding polynomials, are the constant versus the variable terms.

And I think you already know, these are variable terms right here. This is a constant term.is the arithmetic work of Diophantus of Alexandria (c. 3rd century ce).His writing, the Arithmetica, originally in 13 books (six survive in Greek, another four in medieval Arabic translation), sets out hundreds of arithmetic problems with their pfmlures.com example, Book II, problem 8, .

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