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)