Function Question, Algebra 2

1. Consider the function f(x) = x4 – 3x3 – 7x2 + 15x + 18.
a. Find the possible rational roots of f(x) = 0.
b. Use synthetic division to divide f(x) by x – 3. Show all your work. Use your answer to explain whether or not x – 3 is a factor of f(x).
c. Factor f(x) completely. Show all your work.


I have absolutely no idea how to do this! Can anyone explain this to me?? Please and thank you

1. f(x) = x^4 - 3x^3 - 7x^2 + 15x + 18
a. Factors of constant = 1, 2, 3, 6, 9, 18
Factors of leading coefficient = 1
Possible Rational Roots = +/- 1, +/- 2, +/- 3, +/- 6, +/- 9, +/- 18
b. [3] 1 -3 -7 15 18
3 0 -21 -18
1 0 -7 -6 [0]
x^3 - 7x - 6
x - 3 is a factor of f(x).
c. f(x) = (x - 3)(x^3 - 7x - 6)
PRZ = +/- 1, +/- 2, +/- 3, +/- 6
[-1] 1 0 -7 -6
-1 1 6
1 -1 -6 [0]
f(x) = (x - 3)(x + 1)(x^2 - x - 6)
f(x) = (x - 3)(x + 1)(x - 3)(x + 2)
f(x) = (x - 3)^2 (x + 1)(x + 2)