List the negative integral values of x that render the algebraic expression $(x–5)^8 (x–2)^3$ positive.

Correct answer marked below

-4, -5

-3, -4

-2, -5

-1

No negative integral value exists for x

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What this question tests

Your ability to solve and combine linear inequalities and reason about ranges of values.

Failing to flip the inequality sign when multiplying or dividing by a negative, or missing an inclusive/exclusive endpoint.

List the negative integral values of x that render the algebraic expression (x–5)8(x–2)3(x–5)^8 (x–2)^3(x–5)8(x–2)3 positive.