Polynomial comes from poly- (meaning "many") and also -nomial (in this case an interpretation "term") ... So it says "many terms"
Polynomials through one variable do nice smooth curves:
A polynomial can have:
|constants (like 3, −20, or ½)|
|variables (like x and also y)|
|exponents (like the 2 in y2), yet only 0, 1, 2, 3, ... |
You are watching: Is 1/x a polynomial
and so on are allowed
that deserve to be combined using addition, subtraction, multiplication and also division ...
... Except ...
|... not division by a variable (so something choose 2/x is ideal out)|
Also they can have one or more terms, but not one infinite number of terms.
Polynomial or Not?
These are polynomials:
(Yes, "5" is a polynomial, one term is allowed, and it deserve to be just a constant!)
These space not polynomials3xy-2 is not, since the exponent is "-2" (exponents can only be 0,1,2,...) 2/(x+2) is not, due to the fact that dividing by a change is not permitted 1/x is no either
But these are allowed:x/2 is allowed, because you deserve to divide through a constant also 3x/8 for the same factor √2 is allowed, because it is a continuous (= 1.4142...etc)
Monomial, Binomial, Trinomial
There room special names because that polynomials with 1, 2 or 3 terms:
How do you remember the names? Think cycles!
There is additionally quadrinomial (4 terms) and also quintinomial (5 terms),but those names room not regularly used.
Polynomials can have no variable at all
Example: 21 is a polynomial. It has actually just one term, i m sorry is a constant.
Or one variable
Example: x4 − 2x2 + x has actually three terms, however only one change (x)
Or 2 or an ext variables
Example: xy4 − 5x2z has actually two terms, and also three variables (x, y and z)
What is Special around Polynomials?
Because that the strict definition, polynomials are basic to occupational with.
For example we know that:
So you deserve to do too many of additions and multiplications, and also still have a polynomial together the result.
Also, polynomials the one change are straightforward to graph, together they have smooth and constant lines.
See how nice andsmooth the curve is?
You can additionally divide polynomials (but the an outcome may not be a polynomial).
The degree that a polynomial with just one variable is the largest exponent of the variable.
|4x3 − x + 2||The degree is 3 (the largest exponent the x)|
For more facility cases, read degree (of an Expression).
The Standard type for composing a polynomial is to placed the terms with the highest degree first.
See more: Convert 18 Mm Equals How Many Inches, Milimeter To Inches Conversion Chart
Example: placed this in traditional Form: 3x2 − 7 + 4x3 + x6
The highest degree is 6, so the goes first, climate 3, 2 and also then the consistent last:
x6 + 4x3 + 3x2 − 7
You don"t have actually to use standard Form, however it helps.
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