Question

26. Matthew factored a 5th-order polynomial. Four of the factors are: (x-2), (x+2i), (x-4), and (x+4) .

Which of the following is the other factor?
a) (x+2)
b) (x-2)
c) (x-2i)
d) (x+2i)

Could someone show me the steps on how to solve this? Thanks! :)

Answer 1

Short Answer C
Remark
You may think there is no way to resolve this. Either of the first two look like they might work and you cannot be sure what you will get with the last two unless you know.

The answer is one of the last two. The equation cannot have just one or even a large number of complex numbers. When you are factoring a polynomial, the number of complex numbers must be even.

The complex root you have is x + 2i. Its partner is x - 2i
The complete equation would be
y = (x - 2i)(x + 2i) (x - 2)(x + 4)(x - 4)
I'll edit to add the graph.