Question

Factoring with imaginary numbers?

Answer 1

I have to type out what I've already done, one second

Answer 2

Original equation: \[x^{3}-7x^2+11x+19\]
I used synthetic division and p/q to get eventually: (x + 1)(x^{2} - 8x + 19)
I used the Quadratic Formula to get: \[(8 \pm 2\sqrt{3}i) \div2\]

Answer 3

Am I correct? And if so, how do I put that in the correct form? Like (x + 1)(x - ?)(x + ?)

Answer 4

To put it in the proper form, let's look at the + part of the ±.

Answer 5

\[\frac{8 + 2 i \sqrt{3}}{2} \\ 4 + i\sqrt{3}\]
So, the first complex root is \[(x - (4 + i \sqrt{3})\]

Answer 6

Ohhh!

Answer 7

Thank you!