From the factor \(( x + 1 )^2\), we get the zero \(- 1\). Since the zero is of multiplicity two and since \(2\) is an even number, the zero is of even multiplicity. Thus the zero is intransitive. This means that the sign of the factor \(( x + 1 )^2\) does not change at the zero \(- 1\), thus the graph of the function does not cross the \(x\)-axis at \(- 1\).
From the factor \(( x - 1 )\), we get the zero \(1\). Since the zero is of multiplicity \(1\) and since \(1\) is an odd number, \(1\) is a zero of odd multiplicity. Thus it is a transitive zero. The sign of the factor \(( x - 1 )\) changes at \(1\), so the graph of the functions crosses the \(x\)-axis at \(1\).
From the factor \(( x - 2 )^3\), we get the zero \(2\). Since the zero is of multiplicity \(3\) and since \(3\) is an odd number, \(2\) is a zero of odd multiplicity. Thus the sign of the factor \(( x - 2 )^3\) changes at \(2\). So the graph of the function crosses the \(x\)-axis at \(2\). There is a special feature of zeros of odd multiplicity greater than \(1\): The graph not only crosses the \(x\)-axis at the zero, it flattens out to horizontal at the cross-over point.