Question

Use synthetic division to show that x is a solution of the third-degree polynomial equation, and use the result to factor the polynomial completely. List all the real zeros of the function.

x^3 - 28x - 48 = 0 x=2

I have no idea how to start this problem!!

Answer 1

You can check to see that x=-2 checks.

-8+56-48 does indeed equal zero, so x+2 is a factor.

Now divide x+2 into the polynomial (you are asked to use synthetic division) to get the remaining quadratic. Once you have that, you can factor to get the other two roots.