Which expression is a polynomial having only even powers?

Correct answer: \(x^6+2x^4-x^2+9\)

In \(x^6+2x^4-x^2+9\), the powers of \(x\) are \(6,4,2\), and the constant term \(9\) has power \(0\). All of these are even, non-negative integers, so it is a polynomial with only even powers. Option B contains odd powers, while C has a negative power and D has a fractional power because \(\sqrt{x}=x^{1/2}\); hence they are not the required polynomial. Exam tip: in a polynomial, the exponent of a variable must be a non-negative integer.