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A polynomial is a mathematical expression consisting of a sum of terms, each term including a variable or variables raised to a power and multiplied by a coefficient. The simplest polynomials have one variable. A one-variable (univariate) polynomial of degree n has the following form: $$a_nx^n + a_{n-1}x^{n-1} + ... + a_1x^1 + ax^0$$ where the a's represent the coefficients and x represents the variable. Because x1 = x and x0 = 1 for all complex numbers x, the above expression can be simplified to: $$a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a$$ The degree of a polynomial in one variable is the largest exponent in the polynomial. Some polynomials can have two, three, or more variables. A two-variable polynomial is called bivariate; a three-variable polynomial is called trivariate.

**Addition Example:**

Add (4x^{2} + 6x + 7), (3x^{2} - 5x - 10) and (6x + 5)

Line them up in columns and add:

4x^{2 }+ 6x + 7

3x^{2 }- 5x - 10

0x^{2 }+ 6x + 5

_________

7x^{2} + 5x + 2

**Subtraction Example:**

Subtract (3x^{2} - 5x - 10) from (4x^{2} + 6x + 7)

Line them up in columns and subtract:

4x^{2} + 6x + 7

-(3x^{2} - 5x -10)

__________

x^{2} + 11x - 3

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