Question

Polynomial f(x) has x-intercepts at x = 2 , x = -2, x = 3 and x = -3. Write the polynomial in factored form and then multiply the factors to produce a polynomial.

Answer 1

Here's the principle involved:

Each root / x-intercept / zero of a polynomial has a corresponding factor:

x = 2 , x = -2, x = 3 and x = -3 => factors (x-2), (x+2), (x -3), and so on. What is the last factor, the one corresponding to x = -3?

Answer 2

Method: If you have the (invented) factors (x-5), (x+7), the polynomial in question is f(x)=(x-5),+(x+7).
We can multiply that out (hint: use the FOIL method), to obtain
f(x)=x^2 + 2x -35.

Please apply exactly the same techniques to answer the question you've posted.