Question

find the polynomial that has the given zeros.-2, 1, 1, 5

Answer 1

A polynomial having those as "zeroes" means that when the polynomial function f(x) is evaluated at those points, the function goes to zero. The easiest way to find a function that satisfies this is
\[\begin{array}{l}
x=-2 & \longrightarrow & x+2=0
\\x=1 & \longrightarrow & x-1=0
\\ x=1 & \longrightarrow & x-1=0
\\x=5 & \longrightarrow & x-5=0
\end{array}\]
so
\[f(x) = (x+2)(x-1)(x-1)(x-5)\]
You can see that plugging in any of the given "zeroes" of the function makes the function 0.

Simplify that into a 4th degree polynomial to find your solution ^_^