use all available methods(e.g.,Rational Zeros Theorem, Descarte's Rule of Signs,polynomial division, etc.?

Question

consider the following polynomial equation f(x)=3x raised to the 3 -11x raised +2nd power
8x+4
factoered polynomial f(x)=

Answer 1

Assuming the sign in front of the term "8x" is "+":

Use the standard formula for solving cubic equations and obtain the roots 2, 2, and
-1/3.

That last root can be expressed as:
x= -1/3
3x = -1
3x + 1 = 0

Expressing both other roots as:
x = 2
x - 2 = 0

Then combining all three, the factored polynomial is:

(x - 2) (x - 2) (3x + 1)