# A type of problem that we may see will be a problem that asks us if the function is a polynomial function. The answer will be determined by whether or not we have a polynomial. For example, is f(x)...

A type of problem that we may see will be a problem that asks us if the function is a polynomial function. The answer will be determined by whether or not we have a polynomial. For

example, is f(x) = a polynomial function? The answer will depend on whether or not is a polynomial.

please explain if is or is not a polynomial.

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### 1 Answer

A polynomial is an algebraic expression consisting of one or more monomials. A monomial is a number, variable, or the product of a number and one or more variables. If a polynomial contains one or more variables, they are combined with addition or subtraction. A binomial is a polynomial with two monomial terms, such as x+5, x+p or `x^2+x` etc.

A trinomial is a polynomial with three monomial terms such as `x^2+7x-12` , y+yz+xyz.

Therefore, a polynomial is a function of the form

f(x)= `a_nx^n + a_(n-1)x^(n-1) + a_(n-2)x^(n-2) + a_0` , where all the exponents are whole numbers.

A polynomial equation used to describe a function is called a polynomial function.

Polynomial functions of degree one are called linear polynomial functions. Polynomial functions of degree two are called quadratic polynomial functions, and so on.

As is evident from such examples, polynomials often include powers. These powers can be used to classify polynomials by their order. For instance `2x^3 +7x^2+1` is a third order polynomial because the largest exponent is 3. Similarly, `2x^2+3x-sqrt2` is a polynomial of second order.

Therefore, in order to find whether a given function f(x) is a polynomial or not, look at the base and exponents. The base should be variable, and the exponents – all whole numbers.

For example:` x^3 + 3^x` is NOT a polynomial, but `x^3+1` is one.

Similarly `6x^2+2x^-1+7` is NOT a polynomial, because -1 is not a whole number.

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