Which expression is a polynomial in (x) and has only even powers?

Correct answer: \(x^8-5x^6+2x^2+4\)

In \(x^8-5x^6+2x^2+4\), the powers of \(x\) are \(8,6,2\), and \(0\) (for the constant term \(4\)). They are all non-negative integers and even, so it is a polynomial containing only even powers. \(x^7+x^2+1\) is a polynomial, but \(7\) is an odd power. \(x^{-2}+x^4\) and \(x^{1/2}+x^2\) are not polynomials because they contain a negative and a fractional exponent, respectively. Exam tip: powers of the variable in a polynomial must be non-negative integers.