what is a polynomial

What is a polynomial? A polynomial is a math expression made from variables, numbers, and whole-number exponents, combined using addition, subtraction, and multiplication. It cannot have a variable in the denominator, a negative exponent, or a fractional exponent.

Quick Scoop

Examples of polynomials include x2+3x+2x^2+3x+2x2+3x+2 and 5y4−7y+15y^4-7y+15y4−7y+1.

Not polynomials: 1/x1/x1/x, x−2x^{-2}x−2, and x\sqrt{x}x​, because they break the rule about allowed exponents or division by a variable.

Main Idea

Each piece of a polynomial is called a term, and each term has a coefficient and a variable part. The highest exponent in the expression is called the degree of the polynomial.

Simple View

Think of a polynomial like a combination of building blocks:

• Numbers are allowed.
• Variables are allowed.
• Exponents must be whole numbers 0,1,2,3,…0,1,2,3,\dots 0,1,2,3,….

Tiny Example

For x2+4x−7x^2+4x-7x2+4x−7:

• x2x^2x2 is one term.
• 4x4x4x is one term.
• −7-7−7 is one term.
• The degree is 2.

If you want, I can also explain monomial, binomial, and trinomial in one minute.