Question

X^n -27 is divisible by x-3 when n is equal to

Answer 1

xⁿ - 27 is divisible by (x - 3)
∴ (xⁿ - 3³) is divisible by (x - 3)
∴ (x - 3) is a factor of xⁿ - 3³
∴ x = 3 is a root of xⁿ - 27
So, put x = 3 in expression (xⁿ - 3³)
3ⁿ - 3³ = 0
⇒ 3ⁿ = 3³
⇒ n = 3

Hence, answer is n = 3