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

Answer Choices

Correct answer marked below

-4, -5

-3, -4

-2, -5

-1

No negative integral value exists for x

Correct

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Comments

GouriMay 18

thanks, this one was quick once you notice the even power!

KruthiSep 19

Wait, I got confused for a sec. If x is negative, isn't (x-5) always negative? And an even power makes it positive... so then I only need (x-2)^3 to be positive too. But for negative x, (x-2) is negative, so its cube is negative. So the whole thing is negative. That's why no negative works, right?

PaulOct 1

yep exactly, the (x-5)^8 part is always positive so it doesn't matter, and the cubic part flips the sign

What this question tests

What it tests

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

Common trap

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.