Let f(x) := 3x+x 2- 38x+24
(a) Find all the possible rational zeros of f(x) (according to Rational Root Theorem).
(b) Illustrate that x = -4 is a zero (or root) of function f(x) := 3x+x 2- 38x+24 (i.e. show that f(-4) = 0). What does this sigify you about the factor of polynomial function?
(c) Find quotient and remainder when 3x+x 2- 38x+24 is divided by factor you found in part (b). (You may use either polynomial long division or synthetic division to do this.)
(d) Use what you found in parts (a) - (c) to factor polynomial function f(x) := 3x+x 2- 38x+24