61. Let f(x)=x4+2x3−11x2−13x+38.
(a) Use the upper and lower bound tests to prove that all of the real zeros of f lie on the interval [−5,4].
(b) Find all of the rational zeros of f.
(c) Factor f(x) using the rational zero(s) found in (b).
(d) Approximate all of the irrational zeros of f.
(e) Use synthetic division and the irrational zero(s) found in (d) to continue the factorization of f(x) begun in (c).