Question 538327
It's all in your textbook.
TERMS
Polynomials have some plus and/or minus signs separating what we call "terms."
Your polynomial has 4 terms.
A trinomial has 3 terms and a binomial has 2 terms, just like a tricycle has 3 wheels and a bicycle has 2. The prefixes bi-, tri-, or poly- in front of "nomial" tell you that there are 2, 3, or "many" terms (with "many" defined very loosely).
A monomial (mono meaning 1) has only one term.
Your polynomial could be called a quadrinomial (because it has 4 terms), but the word quadrinomial is not used much. You can safely forget that word.
*** Your polynomial is not a trinomial.
COEFFICIENTS
The terms consist of a number, called the coefficient, multiplied by one or more variables with exponents.
DEGREES
Each term has a degree that is the exponent of the variable (or the sum of the exponents of the different variables in the term if there is more than one variable). The degree for 5x^4 is 4. The degree for +8x^3 is 3. The degree for -5x is 1. The degree for +3 is zero.
The degree of the polynomial is the highest of all the degrees of the terms, so
*** the degree of your polynomial is 4.
QUADRATIC, CUBIC
There are special names for polynomials of degree 2 and 3. Polynomials of degree 2 are called quadratic (the mane comes from square in some other language). Quadratic is a very popular word in algebra. Quadratic polynomials that have terms of degree 1 and zero have three terms, and are called quadratic trinomials. If you can say that you'll really sound precocious. Polynomials of grade 3 are called cubic (the name comes from cube). I could explain what a square and a cube have to do with those polynomials, but I have already rambled enough.
*** Your polynomial is not quadratic because it is not of degree 2.
Polynomials are usually written in order of highest to lowest degree, so the highest degree term is usually written first. It is called the leading term, and its coefficient is the leading coefficient.
***** The leading coefficient of your polynomial is 5.