When x² - 5x + p is divided by (x - 2), the remainder is 3. Then the value of p is :

1. 9

2. -9

3. -6

4. 6

By remainder theorem,

If a polynomial p(x) is divided by (x - a), then remainder = p(a).

⇒ x - 2 = 0

⇒ x = 2.

Given,

On dividing x² - 5x + p by (x - 2), remainder = 3.

∴ 2² - 5(2) + p = 3

⇒ 4 - 10 + p = 3

⇒ p - 6 = 3

⇒ p = 3 + 6 = 9.

Hence, Option 1 is the correct option.