3. [3] a) Algorithm 30 in the book explains how to lift a factorization of monic f into two factors from being modulo p to being modulo p". What changes would you need to make here to allow it to handle a non-monic f (the "leading coefficient problem")? b) Again assuming only two factors, what changes would be needed elsewhere to factor a non-monic f Z[:]? [3] c) If f has a much smaller (in particular 1) trailing coefficient than the leading coefficient, is there a better method we can use? If so, explain it. d) Why is the leading coefficient problem so much worse for multivariate polynomials? [2] e) Explain in words and symbols (but not pseudocode) the idea behind Wang's solution (Algorithm 38 in the book) to this problem. f) Might the idea you have developed in part (e) be useful here? [4 3. [3] a) Algorithm 30 in the book explains how to lift a factorization of monic f into two factors from being modulo p to being modulo p". What changes would you need to make here to allow it to handle a non-monic f (the "leading coefficient problem")? b) Again assuming only two factors, what changes would be needed elsewhere to factor a non-monic f Z[:]? [3] c) If f has a much smaller (in particular 1) trailing coefficient than the leading coefficient, is there a better method we can use? If so, explain it. d) Why is the leading coefficient problem so much worse for multivariate polynomials? [2] e) Explain in words and symbols (but not pseudocode) the idea behind Wang's solution (Algorithm 38 in the book) to this problem. f) Might the idea you have developed in part (e) be useful here? [4