For which value will ((4a+8)x-5) not remain linear?

Correct answer: \(a=-2\)

The expression \((4a+8)x-5\) is linear only when the coefficient of \(x\) is non-zero. For it to stop being linear, \(4a+8=0\), which gives \(a=-2\). At this value, the expression becomes \(-5\), a constant polynomial rather than a linear polynomial. For example, at \(a=0\), the coefficient of \(x\) is \(8\), so it is still linear. Exam tip: in a parameter-based linear polynomial, set the coefficient of the variable equal to zero to test when it is no longer linear.