coefficient of x algebraic expression
Answers
Answer:
When there is no numerical factor in a term, its coefficient is taken as +1. For example, in the term x2y3, the coefficient is +1. In the term –x, the coefficient is -1.
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We have learnt how to write a term as a product of factors. One of these factors may be numerical and the others algebraic (i.e., they contain variables). The numerical factor is said to be the numerical coefficient or simply the coefficient of the term. It is also said to be the coefficient of the rest of the term (which is obviously the product of algebraic factors of the term). Thus in 5xy, 5 is the coefficient of the term. It is also the coefficient of xy. In the term 10xyz, 10 is the coefficient of xyz, in the term –7x2y2, –7 is the coefficient of x2y2.
When the coefficient of a term is +1, it is usually omitted. For example, 1x is written as x; 1 x2y2 is written as x2y2 and so on. Also, the coefficient (–1) is indicated only by the minus sign. Thus (–1) x is written as – x; (–1) x2 y 2 is written as – x2 y2 and so on.
Sometimes, the word ‘coefficient’ is used in a more general way. Thus we say that in the term 5xy, 5 is the coefficient of xy, x is the coefficient of 5y and y is the coefficient of 5x. In 10xy2, 10 is the coefficient of xy2, x is the coefficient of 10y2 and y2 is the coefficient of 10x. Thus, in this more general way, a coefficient may be either a numerical factor or an algebraic factor or a product of two or more factors. It is said to be the coefficient of the product of the remaining factors.