# Writing a polynomial in standard form

So, for example, what I have up here, this is not in standard form; because I do have the highest-degree term first, but then I should go to the next highest, which is the x to the third. We are looking at coefficients. Seven y squared minus three y plus pi, that, too, would be a polynomial.

## Standard form of a polynomial calculator

Trinomial's when you have three terms. Seven y squared minus three y plus pi, that, too, would be a polynomial. Well, I don't wanna get too technical. These are examples of polynomials. A polynomial is something that is made up of a sum of terms. You have to have nonnegative powers of your variable in each of the terms. A few more things I will introduce you to is the idea of a leading term and a leading coefficient. We have this first term, 10x to the seventh. This one right over here is a second-degree polynomial because it has a second-degree term and that's the highest-degree term.

This is an example of a monomial, which we could write as six x to the zero. The third coefficient here is It can be, if we're dealing This right over here is a binomial. This is a four-term polynomial right over here. You could even say third-degree binomial because its highest-degree term has degree three.

## Write each polynomial in standard form then give the leading coefficient

Seven y squared minus three y plus pi, that, too, would be a polynomial. If this said five y to the seventh instead of five y, then it would be a seventh-degree binomial. Could be any real number. But in a mathematical context, it's really referring to many terms. So, for example, what I have up here, this is not in standard form; because I do have the highest-degree term first, but then I should go to the next highest, which is the x to the third. Lemme do it another variable. Or, if I were to write nine a to the a power minus five, also not a polynomial because here the exponent is a variable; it's not a nonnegative integer. Sometimes people will say the zero-degree term. Lemme write this word down, coefficient. This is a polynomial. When you have one term, it's called a monomial. If I were to write 10x to the negative seven power minus nine x squared plus 15x to the third power plus nine, this would not be a polynomial.

If I were to write seven x squared minus three. Here, it's clear that your leading term is 10x to the seventh, 'cause it's the first one, and our leading coefficient here is the number Then, negative nine x squared is the next highest degree term.

### Write each polynomial in standard form. identify the leading coefficient

So this is a seventh-degree term. These are really useful words to be familiar with as you continue on on your math journey. Trinomial's when you have three terms. The third coefficient here is Now, the next word that you will hear often in the context with polynomials is the notion of the degree of a polynomial. The second term is a second-degree term. So, plus 15x to the third, which is the next highest degree. So in this first term the coefficient is Nonnegative integer. Then, negative nine x squared is the next highest degree term. So here, the reason why what I wrote in red is not a polynomial is because here I have an exponent that is a negative integer. Trinomial's when you have three terms. So, this right over here is a coefficient. Any of these would be monomials.
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