vikasp99 wrote:

Which of the following must equal zero for all real numbers x ?

I. x^3 - x^2

II. x^0

III x^1

A. None.

B. I only

C. II only

D. I and II only

E. II and III only

This is a MUST question, which means if an expression can be shown to NOT EQUAL ZERO, we can

eliminate it.

I. x^3 - x^2

Test a value.

For example, when x = 2, x^3 - x^2 = 2^3 - 2^2 = 8 - 4 = 4

Since x^3 - x^2 DOES NOT EQUAL ZERO we can

eliminate statement I

II. x^0

Test a value.

For example, when x = 2, x^0 = 2^0 = 1

Since x^0 DOES NOT EQUAL ZERO we can

eliminate statement II

III. x^1

Test a value.

For example, when x = 1, x^1 = 1^1 = 1

Since x^1 DOES NOT EQUAL ZERO we can

eliminate statement III

Answer: A

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