Polynomial functions

Question

Find a fourth-degree polynomial P(x) that has zeros at x = 0, x = 1, x = −1, and x = −5,

 and whose x²-term has coefficient 6.

Answer 1

ax(x-1)(x+1)(x-5)

=ax(x^2-1)(x-5)

=ax(x^3 -5x^2 -x +5)

=a(x^4 -5x^3 -x^2 +5x)

to make the x^2 coefficient =6, a must = -6

=-6(x^4 -5x^3 -x^2 +5x)

P(x) = -6x^4 +30x^3 +6x^2 +30x has the given four zeros and required x^2 coefficient