Which of the following expressions is a linear polynomial in x for every real value of p?

Correct answer: \((p^2+1)x-4\)

For a polynomial to be linear in x, the coefficient of x must never be zero. In option A, \(p^2+1>0\) for every real p, so it always has degree 1. In option B, the coefficient becomes zero at \(p=0\) or \(1\). Exam tip: always test whether a parameter-dependent coefficient can vanish.