"What is the Factor of the expression Kindly provide a solution"

"The expression

is factorable by the factor theorem: since x = 2 is a root (a number which yields 0 when substituted), x - 2 is a factor.

However, dividing x⁷ - 128 by x - 2 gives a quotient which is a sixth-degree polynomial. So, the easiest way to solve for x is by setting x⁷ - 128 equal to 0.

First, we isolate the variable by adding 128 to both sides:

Notice that 128 is a power of 2. Precisely, the seventh power of 2. So, we may rewrite 128 as 2⁷.

By laws of exponents, since the powers are equal, the bases must be equal.

Therefore, x = 2."