![]() |
|
Multiplication of polynomials relies on the distributive
property. The reverse process, where a polynomial is written as a
product of other polynomials, is called factoring. For example,
one way to factor the number 18 is to write it as the product The Greatest Common FactorTo factor the algebraic expression 15m + 45, first note that
both 15 m and 45 are divisible by 15; Both 15 and m+3 are factors of 15m + 45. Since 15 divides into both terms of 15m + 45 (and is the largest number that will do so), 15 is the greatest common factor for the polynomial 15m + 45. The process of writing 15m + 45 as15(m+3) is often called factoring out the greatest common factor. EXAMPLE Factoring Factor out the greatest common factor. (a) 12p - 18q Solution Both 12 p and 18 q are divisible by 6. Therefore, 12p - 18q = 6·2p - 6·3q = 6 (2p -3q) (b) 8x Solution Each of these terms is divisible by x . 8x = x(8x One can always check factorization by finding the product of the factors and comparing it to the original expression. CAUTION When factoring out the greatest common factor in an expression
like 2x 2x |