Question

defination polynomial in one variable with example and counter example​

Answer 1

A polynomial in one variable is a function in which the variable is only to whole number powers, and the variable does not appear in denominators, in exponents, under radicals, or in between absolute value signs or greatest integer signs.

Examples of polynomials in one variable:

• 3x⁴ + x³ +8³

• ( x² + x + 1 ) ( 3x - 8 )

• -6x² - ( 7/9 )x

• 7

Examples of expressions that are not polynomials:

• 2x

• ( x + 1 ) / ( 3x⁴ - 1 )

• 1 / x

• x ( 1/2 )

But these are allowed:

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

• 3x/8 is also allowed for the same reason

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

A polynomial in one variable can have as any terms but the variable should be one only . For example : x4−2x2+x.x4−2x2+x. It has 3 terms but only one variable ,i.e., x .

An example that disproves a statement (shows that it is false). Example: the statement "all dogs are hairy" can be proved false by finding just one hairless dog (the counterexample) like below.

I hope this will help you dear..

Always stay safe and stay healthy..

Answer 2

$\huge{\underline{\mathtt{\red{A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}$

Polynomials in one variable are algebraic expressions that consist of terms in the form axn a xn where n is a non-negative

(i.e. positive or zero)

integer and a is a real number and is called the coefficient of the term.

The degree of a polynomial in one variable is the largest exponent in the polynomial.

$\small\bold\star\mathtt{\fcolorbox{red}{pink}{thanks!!}}$