3.10 Quiz Factor Over The Complex Numbers

Question: Factor the expression over the complex numbers.

x^2 + 18

Answer: (x − 3i√2)(x + 3i√2)

Question: Factor the expression over the complex numbers.

x^2+20

Answer: (x + 2i√5)(x - 2i√5)

Question: Factor the expression over the complex numbers.

x^2 + 36

Answer: (x + 6i)(x - 6i)

Question: Factor the expression over the complex numbers.

y^2 + 49

Answer: (y - 7i)(y + 7i)

Question: Factor the expression completely over the complex numbers.

x^4 − 81

Answer: (x + 3)(x - 3)(x + 3i)(x - 3i)

Question: Factor the expression completely over the complex numbers.

y^4 + 14y^2 + 49

Answer: ((y + i√7)(y - i√7))^2

Question: Factor the expression completely over the complex numbers.

y^3 + 2y^2 + 16y + 32

Answer: (y - 4i)(y + 4i)(y + 2)

Question: Factor the expression completely over the complex numbers.

y^4 − 16

Answer: (y - 2)(y + 2)(y - 2i)(y + 2i)

Question: Factor the expression completely over the complex numbers.

y^4 + 12y^2 + 36

Answer: ((y - i√6)(y + i√6))^2

Question: Factor the expression completely over the complex numbers.

x^3 + 5x^2 + 9x + 45

Answer: (x + 5)(x + 3i)(x -3i)