write down all the solutions of the equation f(x)=0
24 : ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24
Check if one of these 16 fctors is a solution of the equation. I've found x = 2.
Use synthetic division to cancel out the factor (x - 2). I've got:
Solve the quadratic
for x to get the last 2 solutions of the equation
Looks like you can factor out a 3, but 3 doesn't go into 52 evenly.Solve: for .
And it looks like you can't Factor by grouping.
So use the Rational Roots Theorem or Rational Zeros Theorem.
With that, you'll have:
So plug all possible values into the equation to see which ones give you zero.
When you do that, I get and give you zero.