Actually, it is easier to define a polynomial as a function of a variable, x, in the form:
p(x) = anxn + an-1xn-1 + ... + a2x2 + a1x + a0 where n is an integer and the ai are constants. A non-polynomial, then, is any function of x which contains one or more terms in x which are not in the form akxk.
The zero of a polynomial in the variable x, is a value of x for which the polynomial is zero. It is a value where the graph of the polynomial intersects the x-axis.
A polynomial is a sum of monomials - and each monomial may only contain non-negative integer powers of the variables involved. If any other operation is involved (for example, a negative or fractional exponent; equivalent to a variable in the denominator, or a root), you have a non-polynomial.
No. by definition, the polynomial should contain an integer as exponent and square root 1/2 is not an integer.
Basically, a number is transcendental if it isn't the solution of a polynomial equation. An example would be PI.
A polynomial function of a variable,x, can be written as a sum of non-negative integer powers of x. For example, f(x) = 5x5 + 27x2 - 37/3 x + 2.36.
No. By the definition of a polynomial, the powers can only be non-negative integers.
Polynomial vs non polynomial time complexity
Yes, ( y^3 ) is a polynomial. A polynomial is defined as a mathematical expression that consists of variables raised to non-negative integer powers, along with coefficients. In this case, ( y^3 ) has a single variable ( y ) raised to the power of 3, which is a non-negative integer. Thus, it fits the definition of a polynomial.
"Non-polynomial" can mean just about anything... How alike it is with the polynomial depends on what specifically you choose to include.
how alike the polynomial and non polynomial
Yes, ( m - 2 ) is a polynomial. It is a linear polynomial, which is a type of polynomial of degree 1. Polynomials are defined as expressions that consist of variables raised to non-negative integer powers, and ( m - 2 ) fits this definition with the variable ( m ) raised to the first power and a constant term.
See definition of polynomial and monomials. You will see.
The zero of a polynomial in the variable x, is a value of x for which the polynomial is zero. It is a value where the graph of the polynomial intersects the x-axis.
what is non polynomials
Briefly: A polynomial consists only of powers of the variables - ie the variables multiplied by themselves or one another. A non polynomial can include any other function such as trigonometric, exponential, logarithmic etc.
a polynomial with three terms
a polynomial with two terms