Coefficients

Coefficients:

Introduction to coefficient:

In simple terms the meaning of a coefficient is,a factor that contributes to produce a result.In mathematics, a coefficient is a multiplicative factor in some term of an expression (or of a series); it is usually a number, but in any case does not involve any variables of the expression. For instance in

7x2 − 3xy + 1.5 + y

the first three terms respectively have coefficients 7, −3, and 1.5 (in the third term there are no variables, so the coefficient is the term itself; it is called the constant term or constant coefficient of this expression). The final term does not have any explicitly written coefficient, but is usually considered to have coefficient 1, since multiplying by that factor would not change the term. Often coefficients are numbers as in this example, although they could be parameters of the problem, as a, b, and c in

ax2 + bx + c

when it is understood that these are not considered as variables.Also it is defined as the number in front of the variable is called as coefficient. For example 2x is the given expression here the coefficient is 2. The coefficient is usually in numeral with the variable. The expression contains variable and coefficient of the variable.The other way we can learn about a coefficient is by solving few example problems related to coefficient.
Example Problem for the Coefficient:

Example 1:

Find the coefficient of the variables in the given expression:

X + 2y

Solution:

Given that X + 2y

Here x and 2y is the expression with the coefficient

The coefficient of x is 1

The coefficient of y is 2.

Example 2:

Find the coefficient of variables in the given expression:

Y2 + 2y + 3xy +1

Solution:

Given that Y2 + 2y + 3xy +1

Here y2 , 2y, 3xy, is the expression with the coefficient and 1 is with out variable

The 3xy having two variables that two variable consider as a one variable

1 is the constant term of the given expression

The coefficient of y2 is 1

The coefficient of 2y is 2

The coefficient of 3xy is 3

Example 3:

Find the coefficient of variables in the given expression:

Z5 + z + y +6y

Solution:

Given that Z5 + z + y +6y

Here z5, z, y, 6y is the expression with the coefficient

The coefficient of z5 is 1

The coefficient of z is 1

The coefficient of y is 1

The coefficient of 6y is 6.
Example Problem for the Coefficient:

Example 4:

Find the coefficient of variables in the given expression:

X3 + y 5 +2xy + 5yx

Solution:

Given that X3 + y 5 +2xy + 5yx

Here X3, y 5, 2xy, 5yx the expression with the coefficient

The coefficient of x3 is 1

The coefficient of y5 is 1

The coefficient of 2xy is 2

The coefficient of 5yx is 5.

Example 5:

Find the coefficient of variables in the given expression:

100x2 + 2z3 + 102z

Solution:

Given that 100x2 + 2z3 + 102z

Here 100x2, 2z3, 102z the expression with the coefficient

The coefficient of 100x2 is 100

The coefficient of 2z3 is 2

The coefficient of 102z is 102.