Construct a polynomial function with the following properties: third degree, 1 is a zero of multiplicity 1, −4 is the only other zero, leading coefficient is 5.

Answer 1

5(x-1)(x+4)^2

=5(x-1)(x^2 +8x +16)

= 5(x^3 +7x^2 +8x -16)

f(x) = 5x^3 +35x^2 +40x -80