Answer:
f(x) = (x + 6)(x – 2)
Step-by-step explanation:
The roots of a polynomial are the solutions to its factors. This means you can set the factors equal to 0 and the roots are the solution. Working backwards, if the roots are x = -6 and x = 2 then they must have resulted from factors x + 6 and x - 2. This is true since x + 6 = 0 has solution x = -6. And x-2 = 0 has solution x = 2.
So the polynomial has factors (x+6)(x-2). The solution is f(x) = (x + 6)(x – 2).
