The number part when a number and a variable are multiplied together in a term is called the _____.

Solution:

The number part when a number and variable are multiplied together is called a coefficient.

Therefore in the equation 5x + 4y = 10, x and y are variables and 5 & 4 are coefficients.

Let us consider the general definition of a polynomial to understand better what coefficients are.

A function p is a polynomial which is defined as:

p(x) = \(a_{n}x^{n} + a_{n-1}x^{n-1} + a_{n-2}x^{n-2}+.........+ a_{1}x^{} + a_{0}\)

Where n is a non-negative integer and the numbers \(a_{0}, a_{1}, a_{2},....., a_{n}\) are real constants (called the coefficients of the polynomial).

Each coefficient is attached to one variable and may have the same or different values.

It is to be noted again that coefficients in an equation are real and constants.

They have a multiplier effect on the variable to which they are attached.

There are as many coefficients as there are the number of variables.

Let us take another example of a polynomial as x⁴ + 4x³ + 2x² + x + 4.

The coefficients of this equation are 1, 4, 2 and 1 respectively. Coefficient of x⁴ is 1, the coefficient of x³ is 4, the coefficient of x² is 2, and finally the coefficient of x is 1.

The last term i.e. 4 is a constant but it is not a polynomial,

Answer: Coefficient

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The number part when a number and a variable are multiplied together in a term is called the _____.

Summary:

The number part when a number and a variable are multiplied together in a term is called the coefficient.