For which value will ((a-3)x+8) not remain a linear polynomial?

Correct answer: \(a=3\)

For a polynomial to be linear, the coefficient of \(x\) must be non-zero. Here, the coefficient of \(x\) is \(a-3\). On putting \(a=3\), we get \(a-3=0\), so the expression becomes \(8\), a constant polynomial rather than a linear polynomial. For example, when \(a=0\), the coefficient is \(-3\), so it is still linear. Exam tip: in a linear polynomial, the highest power of the variable is 1 and its coefficient must not be zero.