**Class X > Mathematics > Formula**

**1. Remainder theorem**

*If a polynomial f(x) is divided by (x – α) then remainder = f(α)*

**Example:** Find the remainder (Without division) on dividing f(x) by (x + 3) where f(x) = 2x^{2} – 7x – 1

**Solution:-**

X + 3 = 0 or, x = -3

put x = -3 in f(x)

f(-3) = 2(-3)(-3) – (-3) – 1 = 20

Hence, remainder is 20.

**2. Factor theorem**

*(x- α) is a factor of the polynomial f(x) if and only if f(α) = 0*

**Example:** Show that (x – 5) is factors of f(x) where f(x) = 2x^{2} – 11x + 5.

Solution:-

x – 5 = 0 or, x = 5

put x = 5 in f(x)

f(5) = 2(5)(5) – 11(5) + 5 = 50 – 50 = 0

Hence (x – 5) is the factor.