Main Concept

A polynomial is any object created by the addition, subtraction, and multiplication of constants and variables:

  $\left(x-4\right)\cdot \left(y\+5\right)\+2 x\+3 y\+\mathrm{\π}\cdot z$

$x^2\+x\cdot y\+y^2$ 

A monomial is the product of a constant (for example, 5,-90,40) and a number of variables or indeterminates (for example, x, y, z): $$

$5 x^2$

A polynomial can always be written as the sum of a finite number of monomials (or terms). This is called expanded form:

$3 x^{5 }\+3 x^3\+2 x^2-90$

When the same variable occurs more than once in such a term, you can use an exponent to represent this in the product:

$x^2\+y^2$ instead of $x\cdot x\+y\cdot y$

The degree of a term is the sum of the powers of each variable in the term:

The degree of a polynomial is the maximum degree of any of its nonzero terms:

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