Arc De Triomphe

What are Polynomials?

 

     A polynomial in one variable is any function with a constant multiplied by a variable to a non-negative number(meaning it could be zero), whole number power, or the sum or the difference of those things. The constant multiplied by the variable is still known as the coefficient. 

     There are multiple ways to classify a polynomial. You can classify it by it's degree. The degree is the exponent that the coeffecient and x are raised to. So if the equation was f(x)= 4x^3, the degree would be the third degree, or cubic, because the coefficient is being raised to the third power. There are polynomials that have names such as f(x)=x^6, but are just called the 6th degree. As a general rule, f(x)= x^n power, and the degree is the nth degree.

     Besides by the exponent, you can classify a polynomial by it's number of terms. A term in a polynomial is seperated by either an addition or subtraction sign. If a polynomial has onr term, such as f(x)= x^7, it is a monomial. If it has two, it will be a binomial. Polynomials with at least four terms are just called polynomials. 

     To name a polynomial, you combine the degree and the number of terms. So if the equation was f(x)= 3x^3+7, this would be a cubic binomial, because it has two terms(binomial), and an exponent of 3(cubic polynomial).

     Polynomials, just like any set of numbers, can be added together, subtracted from each other, or multiplied. To add polynomials, you combine the like terms(terms with the same variable and exponent). Subtracting polynomials is very similar. The only difference is that you distribute the subtraction sign into one of the polynomials then combine like terms. To multiply polynomials, you use the distributive property, and distribute one term into the next set of polynomials. You do this for each term. Another way to multiple polynomials with only 4 terms is to use FOIL: first, outer, inner, last. You multiplle they first term, then the outer terms, then inner terms, then the last terms. 

     To sum it all up, a polynomial is a function with an exponent that is at least zero. To name a polynomial, you take it's degree number, which is the power x is raised to, and the number of terms, which is the different quantities seperated by an addition or subtraction sign. Polynomials can be added, subtracted, or multiplied. You combine like terms to add and subtract, and to multiply you distribute one term into all the other ones, and do this for every other term, as well.