Answer
It is necessary to include the term 1 because if we do not, the result is not equal to the original polynomial.
Work Step by Step
$3x^{2}-9x+3$ factored is $3(x^{2}-x+1)$.
Without $1$, we get $3x^{2}-9x$.
$3(x^{2}-x)=3x^{2}-9x$
Because there is no $1$, we cannot distribute the $3$ to a third term, which leaves out an essential part of the polynomial.
