The cubic polynomial q(x)=x3−7x+6 is to be examined for possible linear factors.
a. (i) For each of the polynomials (x−1), (x+2) and (x−3), find the value of q(x) at the corresponding value of x.
b. (ii) Identify which of the given linear polynomials, if any, are factors of q(x).
c. (iii) For every linear factor identified in part (ii), divide q(x) by that factor and write the resulting quadratic factor.