What is a polynomial?

Answer 1

A Polynomial is any algebraic expression that consists of more than 2 terms in which the only allowable exponents are whole numbers, the variable is never used as a divisor and never appears under a radical sign. Technically, many consider polynomials to consist of 4 terms or more because 2 and 3 term equations are named.

• Monomial (One term): 3w
• Binomial (Two terms): 3w - 4x
• Trinomial (Three terms): 3w - 4x + 6y
• Polynomial (2-3+ terms): 3w - 4x + 6y + 7z

A polynomial in x is an expression that can be written in the form:a*xn + b*xn-1 + ... + c*x0Where 'n' is a non-negative integer, 'a', 'b', and 'c' are constant scalars, where a ≠ 0.

In algebra class, it is usually written in the form of a function f such as:

f(x) = 3x2 + 4x1 + 1x0 = 3x2+4x+1

Any value of x for which f(x) = 0 is a root of the equation and a zero of the function.

A polynomial is a finite length expression constructed from variables (also known as indeterminates) and constants, by using the operations of addition, subtraction, multiplication, and constant non-negative whole number exponents. For example, x2 − 4x + 7 is a polynomial, but x2 − 4/x + 7x3/2 is not, because its second term involves division by the variable x and also because its third term contains an exponent that is not a whole number.

Answer 2

A polynomial is the sum of terms, called monomials. Each monomial contains a numerical coefficient, and one or more variables, raised to positive and integer powers.