Answer:
Polynomial: [tex]f(x)=(x+1)(x-5)(x+6)^{2}(x-6i) - 800[/tex]
Step-by-step explanation:
Zeros are at 5, (-2 * 3 = -6), (-3 * 2 = -6), (3i * 2 = 6i)
= 5, -6, -6, and 6i
The factors are (x-5), (x-(-6)), (x-(-6)), (x-6i)
= (x-5), (x+6), (x+6), (x-6i)
For f(-1) = -800, x = -1 which gives a factor of (x - (-1)) = x + 1. The remainder is -800
The polynomial is thus:
f(x) = (x+1)(x-5)(x+6)(x+6)(x-6i) - 800
[tex]f(x)=(x+1)(x-5)(x+6)^{2}(x-6i) - 800[/tex]
