math question?

Question

Make up a polynomial that has the following characteristics: crosses the y-axis at -1, 4 and touches (but bounces back off) the x-axis at -3 and 6.

Answer 1

A polynomial cannot cross the y-axis in two different places.

Answer 2

if you meant that it crosses the x-axis at -1 and 4:
f(x)=(x+1) (x-4) (x+3)^2 (x-6)^2
if you actually meant what you wrote, then there is NO such polynomial!'

Answer 3

Good call, David.

Also, something that touches and bounces off indicates a repeated root.