English, asked by Goals786, 7 days ago

hi .. hello
what is a polynomial ? ​

Answers

Answered by juveriaridha653
0

Polynomial comes from poly- (meaning "many") and -nomial (in this case meaning "term") ... so it says "many terms.

A polynomial can have:

constants (like 3, −20, or ½)

variables (like x and y)

exponents (like the 2 in y2), but only 0, 1, 2, 3, ... etc are allowed

that can be combined using addition, subtraction, multiplication and division ...

... except ...

... not division by a variable (so something like 2/x is right out)

So:

A polynomial can have constants, variables and exponents,

but never division by a variable.

Also they can have one or more terms, but not an infinite number of terms.

These are polynomials:

   3x

   x − 2

   −6y2 − ( 7 9 )x

   3xyz + 3xy2z − 0.1xz − 200y + 0.5

   512v5 + 99w5

   5

(Yes, "5" is a polynomial, one term is allowed, and it can be just a constant!)

These are not polynomials

   3xy-2 is not, because the exponent is "-2" (exponents can only be 0,1,2,...)

   2/(x+2) is not, because dividing by a variable is not allowed

   1/x is not either

   √x is not, because the exponent is "½" (see fractional exponents)

But these are allowed:

   x/2 is allowed, because you can divide by a constant

   also 3x/8 for the same reason

   √2 is allowed, because it is a constant (= 1.4142...etc)

Monomial, Binomial, Trinomial

There are special names for polynomials with 1, 2 or 3 terms:

monomial, binomial, trinomial

There is also quadrinomial (4 terms) and quintinomial (5 terms),

but those names are not often used.

Variables

Polynomials can have no variable at all

Example: 21 is a polynomial. It has just one term, which is a constant.

Or one variable

Example: x4 − 2x2 + x   has three terms, but only one variable (x)

Or two or more variables

Example: xy4 − 5x2z   has two terms, and three variables (x, y and z)

What is Special About Polynomials?

Because of the strict definition, polynomials are easy to work with.

For example we know that:

   If you add polynomials you get a polynomial

   If you multiply polynomials you get a polynomial

So you can do lots of additions and multiplications, and still have a polynomial as the result.

Also, polynomials of one variable are easy to graph, as they have smooth and continuous lines.

Example: x4−2x2+x

x^4-2x^2+x

You can also divide polynomials (but the result may not be a polynomial)

Polynomial comes from poly- (meaning "many") and -nomial (in this case meaning "term") ... so it says "many terms"

Polynomials with one variable make nice smooth curves:

algebra girl

A polynomial can have:

constants (like 3, −20, or ½)

variables (like x and y)

exponents (like the 2 in y2), but only 0, 1, 2, 3, ... etc are allowed

that can be combined using addition, subtraction, multiplication and division ...

... except ...

... not division by a variable (so something like 2/x is right out)

So:

A polynomial can have constants, variables and exponents,

but never division by a variable.

Also they can have one or more terms, but not an infinite number of terms.

Polynomial or not?

These are polynomials:

   3x

   x − 2

   −6y2 − ( 7 9 )x

   3xyz + 3xy2z − 0.1xz − 200y + 0.5

   512v5 + 99w5

   5

(Yes, "5" is a polynomial, one term is allowed, and it can be just a constant!)

These are not polynomials

   3xy-2 is not, because the exponent is "-2" (exponents can only be 0,1,2,...)

   2/(x+2) is not, because dividing by a variable is not allowed

   1/x is not either

   √x is not, because the exponent is "½" (see fractional exponents)

But these are allowed:

   x/2 is allowed, because you can divide by a constant

   also 3x/8 for the same reason

   √2 is allowed, because it is a constant (= 1.4142...etc)

Monomial, Binomial, Trinomial

There are special names for polynomials with 1, 2 or 3 terms:

monomial, binomial, trinomial.

There is also quadrinomial (4 terms) and quintinomial (5 terms),

but those names are not often used.

Degree

The degree of a polynomial with only one variable is the largest exponent of that variable.

Example:

4x3 − x + 2  The Degree is 3 (the largest exponent of x)

For more complicated cases, read Degree (of an Expression).

Standard Form

The Standard Form for writing a polynomial is to put the terms with the highest degree first.

Example: Put this in Standard Form: 3x2 − 7 + 4x3 + x6

The highest degree is 6, so that goes first, then 3, 2 and then the constant last:

x6 + 4x3 + 3x2 − 7

You don't have to use Standard Form, but it helps.

(  LEARN SOMETHING IS YOUR CLASS )

Answered by Bookworm786
0
The ans is —

Polynomials is an algebraic expression in which the powers of the variable are whole numbers(0,1,2,3,…)

Examples : 1. 6 is Polynomial because the power of 6 is 1
2. 2xsquare is a polynomial because the power of x is 2
3. Root y + 5 is not a polynomial because the power of y is half.
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