By definition, a Perfect square is a number that is the square of an Integer.
In this case, you have the following expression given in the exercise:
You can identify that:
Therefore, it is a Perfect square.
Notice that:
Therefore, it is a Perfect square.
For this case you must apply the Difference of two squares is:
Then, you can factor the expression:
The answers are:
- Factored expression:
- ´Perfect squares:
now, this polynomial has roots of 3-i and 4i, namely 3 - i and 0 + 4i.
let's bear in mind that a complex root never comes all by her lonesome, her sibling is always with her, the conjugate, so if 3 - i is there, 3 + i is also coming along, likewise if 0 + 4i is there, her sibling 0 - 4i is also there.