Question

1. Factor the expression over the complex numbers.

Answer 1

1. (x² + 24) factors as the difference of two squares (x² - (-24)) where -24 is the square of the complex number i√24 = 2i√6. The factoring is
  (x - 2i√6)(x + 2i√6)

2. The square of half the coefficient of the x-term needs to be added: 4.5² = 20.25
This number goes in both boxes.

3. This is the square of (y² +20), so the factorization is similar to that for problem 1.
  y⁴ + 40y² + 400 = (y² + 20)² = (y -2i√5)²(y +2i√5)²