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What is the Factor of the expression [tex]x^{7} - 128[/tex]
Kindly provide a solution

Sagot :

Piyanistaidn

The expression

[tex]{x}^{7} - 128[/tex]

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.

[tex] {x}^{7} - 128 = 0[/tex]

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

[tex] {x}^{7} = 128[/tex]

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

[tex] {x}^{7} = {2}^{7} [/tex]

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

Therefore, x = 2.

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