## Related Words

# Numerical Coefficient

## 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:

a_{1}x_{1} + a_{2}x_{2} + ................a_{n}x_{n
}where a_{1},a_{2}...................,a_{n} are numerical
coefficients.

Numerical Coefficient is more frequently referred as Coefficient.

### Example of Numerical Coefficient

The numerical coefficient for the term 10x^{4} is 10.

The numerical coefficients for the expression 3x^{2} + x + 1 are 3, 1, and
1.

### Video Examples: Numerical Coefficients

### Solved Example on Numerical Coefficient

####
**Ques: **Find the numerical co-efficient in the product of (24a^{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})x ab^{2}c x 82*a*^{2}*b*^{2}*c*=

(24 x x 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.