Find polynomial degrees

Question

find a polynomial of the specified degree that satisfies the given condition degree 4 zeros -4 0, 1 ,5 coefficient of x^3 is 4

Answer 1

4(x+4)(x-0))(x-1)(x-5)= 4(x^2-x)(x^2-x-20) = 4x^4 - 8x^3 -76 x^2 -+80x

change the sign of each zero, then stick an x in front of it, multiply them all together, along with 4 in front

to get a 4th degree polynomial with leading coefficient of 4