Definitions:

Factoring a polynomial is expressing the polynomial as a product of two or more factors; it is somewhat the reverse process of multiplying.

To factor polynomials, we generally make use of the following properties or identities; along with other more techniques.

Distributive Property:

$$ab + ac = a ( b + c )$$ Difference of two squares: $$a^2 - b^2 = ( a – b ) ( a + b)$$ Sum of two cubes: $$a^3 + b^3 = ( a + b ) ( a^2 - 2ab + b^2 )$$ Difference of two cubes: $$a^3 - b^3 = ( a - b ) ( a^2 + 2ab + b^2 )$$

Distributive Property: $$3x + 3y = 3 ( x + y )$$ Difference of two squares: $$x^2 - 9= ( x  –  3 ) ( x + 3)$$ Sum of two cubes: $$x^3 +  8^3 = ( x + 2 ) ( x^2 -  4x +  4^2 )$$ Difference of two cubes: $$x^3 -  27^3 = ( x - 3 ) ( x^2 +  6x +  9^2 )$$

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

FOIL for multiplying binomials

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Example: Basic grouping

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Factor Polynomials Using the GCF

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Factoring and the Distributive Property

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Factoring quadratic expressions

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