Definitions:

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 (4x² + 6x + 7), (3x² - 5x - 10) and (6x + 5)
Line them up in columns and add:

4x² + 6x + 7

3x² - 5x - 10

0x² + 6x + 5

_________

7x² + 5x + 2

Subtraction Example:
Subtract (3x² - 5x - 10) from (4x² + 6x + 7)  
Line them up in columns and subtract:

4x² + 6x + 7

-(3x² - 5x -10)

__________

x² + 11x - 3

Polynomials will show up in pretty much every section of algebra and it is important that you understand them.

Combining like terms and the distributive property

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Combining Like Terms 1

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Combining Like Terms 2

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Combining Like Terms 3

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Addition and Subtraction of Polynomials

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Subtracting Polynomials

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