Polynomials?

Question

Make up a polynomial that has the following characteristics: crosses the x-axis at -1 and 4, touches the x-axis at 0 and 2, and is above the x-axis between 0 and 2.

Answer 1

crosses the x-axis at -1 (x+1)
crosses the x-axis at +4 (x-4)
touches the x-axis at 0 (x^2)
touches the x-axis at 2 (x-2)^2

(x+1)(x-4)(x-2)(x-2)x^2
multiply it out to get a sixth degree polynomial.
Check that the values are positive between 0 and 2; if not, change the signs throughout