If a polynomial function has integer coefficients, then every rational zero will have the form p/q where p is a factor of the constant and q is a factor of the leading coefficient.
The possible roots of the polynomial function are every combination of +- p/q
Substitute the possible roots one by one into the polynomial to find the actual roots. Simplify to check if the value is 0, which means it is a root.
(3)^3 - 2(3)^2 - 2(3) -3
Simplify the expression. It is equal to 0 so x=3 is a root of the polynomial.
Since 3 is a root, divide the polynomial by (x-3) to find the quotient polynomial. This polynomial can be used to find the remaining roots.
After completing division, we are left with x^2+x+1.
Set this equation to zero.
x^2 +x+1 =0
Use the quadratic formula to find the solutions. a=1, b=1, c=1
x= -1+i (sq.rt3)/2 and -1-i (sq.rt3)/2
These are the roots of the polynomial x^2-2x^2-2x-3.