Question

(x^n-27) is divisible by (x-3), when n=?

Answer 1

here, given that (x - 3) is a factor of (xⁿ - 27).
f(x) = (xⁿ - 27)
f(3) = 3ⁿ - 27
0 = 3ⁿ - 27
3ⁿ = 27
3ⁿ = 3³
n = 3
hence, we get valus of n = 3

$VERIFICATION:-$

(xⁿ - 27)/(x - 3)

(x³ - 27)/(x - 3)

(x³ - 3³)/(x - 3)

(x - 3)(x² + 9 + 3x)/(x - 3)

(x² + 9 + 3x)
hence, (x - 3) is a factor of (xⁿ - 27) [if n = 3]

Answer 2

Answer:

3

Step-by-step explanation:

here, given that (x - 3) is a factor of (xⁿ - 27).

f(x) = (xⁿ - 27)

f(3) = 3ⁿ - 27

0 = 3ⁿ - 27

3ⁿ = 27

3ⁿ = 3³

n = 3