mult_poly

# mult_poly - Multiplication of polynomials Some terminology...

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Multiplication of polynomials Some terminology . Consider the expression + - + + a 2 b 2 a c 5 a 3 d a c d 3 3 7 , where a , b , c and d are (unknown) real numbers. a , b , c and d are the variables in the expression. This expression is the sum of the three terms : a 2 b , 2 a c , - 5 a 3 d , a c d 3 , 3 7. Each of these terms has a numerical factor called the coefficient of the term The coefficient of - 5 a 3 d is - 5 while the coefficient of the term a c d 3 is 1 3 . 3 7 is a constant term as it does not contain a variable. Since each term in the expression is a constant coefficient times a product of variables raised to a positive integer power, it is a polynomial in the variables that occur. A polynomial with exactly two terms is called a binomial , while a polynomial with three terms is called a trinomial . Multiplication of polynomials . Multiplication of polynomials can be achieved by using the distributive property of multiplication over addition. For example, two binomials + a b and + c d can be multiplied as follows. = ( ) + a b ( ) + c d + ( ) + a b c ( ) + a b d = + + + a c b c a d b d . The first step uses distributivity of multiplication over addition on the left. In more detail, if = S + a b . = ( ) + a b ( ) + c d S . ( ) + c d = + S . c S . d = + ( ) + a b c ( ) + a b d . Alternatively, we can start by using distributivity of multiplication over addition on the right. = ( ) + a b ( ) + c d + a ( ) + c d b ( ) + c d = + + + a c a d b c b d . In more detail, if = T + c d , the first step is: = ( ) + a b ( ) + c d ( ) + a b . T = + a . T b . T = + a ( ) + c d b ( ) + c d . The first term term a c in the product is obtained by multiplying the first (F) terms a and c of the two binomials and the last term b d in the product is obtained by multiplying the last (L) terms b and d of the two binomials. The term a d is obtained by multiplying the " outer " (O) terms a and d together while the term b c is obtained by multiplying the " inner " (I) terms b and c together. The memnonic FOIL , with each letter standing for one of the four terms in the product, can be used to help remember how to multiply binomials. If the variables

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## This note was uploaded on 11/12/2011 for the course MATH 111 taught by Professor Uri during the Spring '08 term at Rutgers.

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mult_poly - Multiplication of polynomials Some terminology...

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