4-4 Factoring Quadratic Expressions

Objectives

To find common and binomial factors of quadratic expressions

To factor special quadratic expressions

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Factors of a given number are numbers that have a product equal to the given number. Factors of a given expression are expressions that have a product equal to the given expression. Factoring is rewriting an expression as a product of its factors.

Essential Understanding You can factor many quadratic trinomials ( a x 2 + b x + c ) open eh , x squared , plus b x plus c close  into products of two binomials.

You can use the Distributive Property or the FOIL method to multiply two binomials. You can use FOIL in reverse to help you factor.

( x + 4 ) ( x + 2 ) = ( x + 4 ) ( x ) + ( x + 4 ) ( 2 ) Use the Distributive Property.   = x ( x ) + 4 ( x ) + x ( 2 ) + 4 ( 2 )   = x 2 + 6 x + 8 table with 3 rows and 3 columns , row1 column 1 , open x plus 4 close open x plus 2 close , column 2 equals open x plus 4 close open x close plus open x plus 4 close open 2 close , column 3 cap use the cap distributive cap property. , row2 column 1 , , column 2 equals x open x close plus 4 open x close plus x open 2 close plus 4 open 2 close , row3 column 1 , , column 2 equals , x squared , plus 6 x plus 8 , end table

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To factor x 2 + 6 x + 8 , x squared , plus 6 x plus 8 comma  think of FOIL in reverse. Find two binomials for which the first terms have the product x 2 , x squared , comma  the products of the outer and inner terms have the sum 6x, and the last terms have the product 8.

x 2 + 6 x + 8 = ( x + 4 ) ( x + 2 ) x squared , plus 6 x plus 8 equals open x plus 4 close open x plus 2 close

When you factor, a table of the different possible factors of the constant term may be helpful.

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