**Definition of Numerical Coefficient**

- The constant multiplicative factors attached to the variables in an expression are known as Numerical Coefficient.

**More about Numerical Coefficient**

- The Numerical Coefficient is always written in front of the variable as shown in the expression given below:

, where are numerical coefficients. - Numerical Coefficient is more frequently referred as Coefficient.

**Example of Numerical Coefficient**

- The numerical coefficient for the term 10
*x*^{4}is 10. - The numerical coefficients for the expression 3
*x*^{2 }+*x*+ 1 are 3, 1, and 1.

**Solved Example on Numerical Coefficient**

Find the numerical co-efficient in the product of (24

a^{2}b^{2}c^{2}), (ab^{2}c), and (82a^{2}b^{2}c).

Choices:

A. - 656

B. 656ab^{2}c

C. - 5904

D. 656

Correct Answer: A

Solution:

Step 1:Given terms are (24a^{2}b^{2}c^{2}), (ab^{2}c), and (82a^{2}b^{2}c).

Step 2:Product of the given terms is:

24a^{2}b^{2}c^{2 }×ab^{2}c× 82a^{2}b^{2}c

= (24 × × 82) (a^{2}b^{2}c^{2}×ab^{2}c×a^{2}b^{2}c)

[Use Associative and Commutative properties.]

Step 3:= (8 × -1 × 82) (a^{2+1+2}b^{2+2+2}c^{2+1+1}) [Simplifying.]

Step 4:= (- 656) (a^{5}b^{6}c^{4}) [Simplifying.]

Step 5:Hence, the numerical coefficient in the product is - 656.

**Related Terms for Numerical Coefficient**

- Coefficient
- Expression
- Factor
- Term