For which value will ((k-6)x+2) be a linear polynomial?

Correct answer: \(k\ne 6\)

In \((k-6)x+2\), the coefficient of \(x\) is \(k-6\). For a polynomial to be linear, the coefficient of \(x\) must be non-zero; hence \(k-6\ne 0\), or \(k\ne 6\). At \(k=6\), the expression becomes \(2\), which is a constant polynomial, not a linear polynomial. Exam tip: for a parameter-based linear polynomial, check that the coefficient of the variable is not zero.