#### Mathematics (NTSE/Olympiad)

# Polynomial

__Factors and coffieients __

**What is a Factor :**

Each combination of the constants and variables, which form a term, is called a factor.

For examples :

(i) 7, x and 7x are factors of 7x, in which 7 is constant (numerical) factor and x is variable (literal) factor.

(ii) In –5x^{2}y, the numerical factor is –5 and literal factors are : x, y, xy, x^{2} and x^{2}y.

**What is a Coefficient : **

Any factor of a term is called the coefficient of the remaining term.

For example :

(i) In 7x ; 7 is coefficient of x

(ii) In –5x^{2}y; 5 is coefficient of –x^{2}y or we can also say –5 is coefficient of x^{2}y.

**Example: Write the coefficient of : **

(i) x^{2} in 3x^{3} – 5x^{2} + 7

** (ii) xy in 8xyz**

** (iii) –y in 2y**^{2} – 6y + 2

** (iv) x**^{0} in 3x + 7

**Solution:**

(i) –5

(ii) 8z

(iii) 6

(iv) Since x^{0} = 1, Therefore 3x + 7 = 3x + 7x^{0}. Therefore, the coefficient of x^{0} is 7