Analyse a parameterised polynomial family

The degree and leading coefficient remain unchanged, and at each input the output differs from \(-\frac{2}{3}(x+1)(x+\frac{3}{4})(x)(x-\frac{1}{2})^{2}\) by the same parameter value

Changing \(t\) changes only the label of the member; all polynomial outputs and coefficients stay unchanged

The roots and coefficients found for the member with \(t=1\) can be used unchanged for every other member

Use \(t\) in place of \(x\) at every step; the input and the family value need not be kept separate