f(x) is the given function. I'll try to help you with the first one, and hopefully you'll understand how to do it from there.
Plug in -2 whenever you see x
, might be off on the arithmetic
Do the same for the other values, just plug in the given value whenever you see a x and simplify.
Polynomial Long Division
Here is a website that shows you how to do polynomial long division.
If there is no remainder, than the divisor is a factor of the entire polynomial. (e.g. 24/3 = 8, no remainder, so 3 is a factor)
To factor the polynomial, you divide it by its factors, and you are already given one. Divide first by , and you will get a quadratic equation of the form , and that should be simply to factor.
Once you have it all factored, say it turns out to be something like (2x-1)(x+3)(x-2). Set this equal to 0, and solve for x
This is only true when any one of the factors is 0,so you have
Solving these for x, we see that