please help with polynomial graphs

Question

https://gyazo.com/1d950c2c6b62e31c25dbace1a3629b3d?token=4762854e4af78c85f11359f012b298e1

Answer 1

Since the graph is ascending the polynomial is of odd degree.

Four zeroes are indicated, -4, -2, 2, and 4. One must be repeated. Since 4 "kisses" the axis it is 4.

P(x) = a(x + 4)(x+ 2)(x - 2)(x - 4)²