Description
The first term in the polynomial, when it is written in decreasing order, is also the term with the biggest exponent, and is called the "leading term".
The exponent on a term Polynomials are usually written this way, with the terms written in "decreasing" order; that is, with the largest exponent first, the next highest next, and so forth, until you get down to the plain old number.
Any term that doesn't have a variable in it is called a "constant" term because, no matter what value you may put in for the variable x, that constant term will never change. In the picture above, no matter what x might be, 7 will always be just 7.m tells you the "degree" of the term. For instance, the leading term in the above polynomial is a "second-degree term" or "a term of degree two". The second term is a "first degree" term. The degree of the leading term tells you the degree of the whole polynomial; the polynomial above is a "second-degree polynomial". Here are a couple more examples:When a term contains both a number and a variable part, the number part is called the "coefficient". The coefficient on the leading term is called the "leading" coefficient.
The "poly" in "polynomial" means "many". I suppose, technically, the term "polynomial" should only refer to sums of many terms, but the term is used to refer to anything from one term to the sum of a zillion terms. However, the shorter polynomials do have their own names:
Polynomials are also sometimes named for their degree:
There are names for some of the higher degrees, but I've never heard of any names being used other than the ones I've listed.
By the way, yes, "quad" generally refers to "four", as when an ATV is referred to as a "quad bike". For polynomials, however, the "quad" from "quadratic" is derived from the Latin for "making square". As in, if you multiply length by width (of, say, a room) to find the area in "square" units, the units will be raised to the second power. The area of a room that is 6 meters by 8 meters is 48 m2. So the "quad" refers to the four corners of a square, from the geometrical origins of parabolas and early polynomials.
Example
"Evaluating" a polynomial is the same as evaluating anything else: you plug in the given value of x, and figure out what y is supposed to be. For instance:
Evaluate 2x3 – x2 – 4x + 2 at x = –3
I need to plug in "–3" for the "x", remembering to be careful with my parentheses and the negatives:
2(–3)3 – (–3)2 – 4(–3) + 2
= 2(–27) – (9) + 12 + 2
= –54 – 9 + 14
= –63 + 14 = –49