Find a possible formula for a fourth degree polynomial g tha

Find a possible formula for a fourth degree polynomial g that has a double zero at -1, g(-4) = 0, g(4) = 0, and g(0) = -2. g(x) =

Solution

zeros : x = -1 ( multiplity 2)

x = -4 ; (multiplicity 1)

x = 4 ; ( multiplicity 1)

Y intercept : (0, -2)

g(x) = k(x+1)^2(x+4)(x- 4)

-2 = k(1)(4)(-4)

k = 2/16 = 1/8

g(x) = (1/18)(x+1)^2(x+4)(x- 4)