FACTORIZATION What is Factorization in Mathematics Factorization of an algebraic expression means writing the given expression as a product of its factors These factors can be numbers variables or an algebraic expression To the factor A number means to break it up into numbers that can be multiplied to get the original number Factors are the numbers algebraic variables or an algebraic expression which divides the number or an algebraic expression without leaving any remainder What is a Factor For example factor of 9 is 1 3 9 Properties of Factors number Fun Facts about Factors 1 All integers have a finite number of factors 2 A number s factor is always less than or equal to the number it can never be bigger than the 3 Except for 0 and 1 every integer has a minimum of two factors 1 and the number itself 4 Factors are found by employing division and multiplication 1 Factors are never decimals or fractions they are only whole numbers or integers 2 All even numbers have 2 as a factor 3 5 is a factor for all numbers that end in 0 and 5 4 All numbers higher than 0 and ending in a 0 have 2 5 and 10 as factors 5 Factoring is a common way to solve or simplify algebraic expressions What is factorization also known as Another name for factorization method is Doolittle s Method as Doolittle s method is basically an algorithm of Factorization method 5 Factorization can be viewed as matrix form of Gauss Elimination method Why do we use factorization It can be used for many things like helping perform arithmetic operations Another way to use factorization is to find the least common multiple and greatest common factor Examples 3x2 5x 2 3x2 5x 2 3x2 6x x 2 3x x 2 x 2 3x x 2 1 x 2 x 2 3x 1 Types of Factoring polynomials 1 GreatestFactor GCF 2 Grouping Method 3 Sum or difference in two cubes 4 Differenceuares method 5 General trinomials 6 Trinomial method 1 GCF Always take out the greatest common factor first a 6x2y3 10xy5 2xy3 3x 5y2 b x y a4b9c x y a2bc5 x y a2bc a2b8 c4 2 Difference of two squares a2 b2 a b a b a 9x2 49y2 3x 7y 3x 7y b 121x2 64 11x 8 11x 8 c 3x2 12 3 x2 4 3 x 2 x 2 d 3h2 48 3 h2 16 3 h 4 h 4 3 Trinomial whose leading coefficient is one and The second is the sum the third is the product a 3x2 18x 24 3 x2 6x 8 3 x 4 x 2 b a2b2 4ab 96 ab 8 ab 12 4 Sum of two cubes a3 b3 a b a2 ab b2 SOAP Same Opposite Always Positive a X3 125 x 5 x2 5x 25 b 27x3 8 3x 2 9x2 6x 4 c 1000c3 343b3 10c 7b 100c2 70bc 49b2 d 8x3 729 2x 9 4x2 18x 81 5 Perfect Square Trinomials a2 2ab b2 a b 2 a 9x2 30x 25 3x 5 3x 5 b 36c2 132cd 121d2 6c 11d 6c 11d 6 Factor by Grouping a b3 3b2 4b 12 b 3 b2 4 b cm3 dm3 8c 8d m3 c d 8 c d m 2 m2 2m 4 c d Good Luck