has a zero so is a factor. That's the special case of the Remainder Theorem; since we'll get a remainder of zero when we divide by
At this point we can just divide or we can try more little numbers in the function. It doesn't take too long to discover too, so is a factor too by the remainder theorem. I can find the third zero as well; but let's say that's out of range for most folks.
So far we have
where is the zero we haven't guessed yet. Again we could divide by but just looking at the constant term we must have
so
We check
We usually talk about the zeros of a function and the roots of an equation; here we have a function whose zeros are