Question

Identify the numerical coefficients of terms (other than constants) in the following expression x+2xy+3y.

Answer 1

Hint: We know algebraic expression is a collection or combination of constant and variables of one or more terms, which are separated by fundamental operations \[\left( { + , - , \times and \div } \right)\]For example, 7b+5m.
Each part of an algebraic expression which is separated by (+) and (-) is called the ‘term’ of an algebraic expression. When a term is made up of constant multiplied by a variable, that constant is called the coefficient of that variable. For example: In 3x, 3 is called coefficient of x.

Complete step-by-step solution:
Given polynomial is: \[x + 2xy + 3y........(1)\]
General equation of the polynomial is \[axy + by + cx\], where a, b and c are the coefficients of the polynomial.
In the equation the terms in the polynomial are x and y.
Coefficient of x and y is a in the first term.
Coefficient of y is b in the second term.
Coefficient of x is 3 in the third term.
Similarly,
In the polynomial (1) the terms are x, 2xy and 3y.
Coefficient of xy is 2 in the second term.
Coefficient of y is 3 in the third term.
Coefficient of x is 1 in the first term.
Let us write them in a tabular manner:

Terms	variables	coefficients
\[x\]	\[x\]	1
\[2xy\]	\[xy\]	2
\[3y\]	\[y\]	3

Note: Terms are added or subtracted to expression and terms can be split into factors. For example: 3x+2y. 2y is term factors are 2 and y. Numerical coefficients of x and y are 3 and 2 respectively.