Step-by-step explanation:
If -5 is a zero, then one of the factors must be (x+5). Typically, a problem will give you one complex root (zero), but you must infer that its conjugate is always another root. In this case, since 2+6i is a root, then 2-6i must also be a root.
Those factors must then be (x-(2+6i)) and (x-(2-6i))
To get the final polynomial, multiply the factors together: (x+5)(x-2-6i)(x-2+6I)
I would multiply the complex factors first since they will typically simplify to a more workable expression.
(x - 2 - 6i)(x - 2 + 6i) = x2 - 2x + 6xi - 2x + 4 - 12i - 6xi + 12i - 36i2
= x2 - 4x + 40
Then multiply this trinomial by the final factor: (x2 - 4x + 40)(x + 5)
= x3 + 5x2- 4x2- 20x + 40x + 200
= x3 + x2 + 20x + 200
To get a coefficient of 3, multiply this polynomial by 3.
3(x3 + x2 + 20x + 200) = 3x3 + 3x2 + 60x + 600
Answer: 3x3 + 3x2 + 60x + 600
