The curve y=(X+3)(5-x) cuts the X-axis at point P and Q, and the y-axis at point R. What is P,Q,R?

First you need to get out of the habit of hitting the Shift key when typing math. X is not x and a math program will not tell you that you made a mistake, it will just give you a goofy answer.

y = -x^2 + 2x + 15 is a parabola. It looks like this: www.wolframalpha.com/input/?i=plot+y+%3D+-x%5E2+%2B+2x+%2B+15

Now study this page until it seems obvious: en.wikipedia.org/wiki/Polynomial_remainder_theorem

The x intercepts are x = -3 and x = 5.

Everything else you might want to know is found at wikipedia.org by typing "parabola" into the search box.