Which expression is a polynomial in (x) if (b) is treated as a constant?

Correct answer: \(bx^4-3bx+2\)

When \(b\) is treated as a constant coefficient, the powers of \(x\) in \(bx^4-3bx+2\) are \(4,1\), and \(0\). All are non-negative integers, so it is a polynomial in \(x\). Option B has \(\frac{1}{x}=x^{-1}\), and option C has \(x^{-4}\); both contain negative powers. In option D, \(\sqrt{x}=x^{1/2}\), which gives a fractional power. Exam tip: powers of the variable in a polynomial can only be \(0,1,2,\ldots\).