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
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)
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)