Find maximum number of real zeros of f. Then list potential rational zeros of function

Question

f(x)=-3x^3-x^2+x+10

Answer 1

Set f(x) equal to zero.

 

-3x³ - x² + x + 10 = 0

 

 

The possible zeros, according to the rational root theorem are

 

c = ±1, ±2, ±5, ±10, ±1/3, ±2/3, ±5/3, ±10/3.

 

 

Use synthetic division to test these zeroes. The quotient must have a reminder of zero.

 

Or you can evaluate f(c).  f(c) = 0   where x=c.