Question

How do you write `x^4 + 13x^2 + 36` as a product of linear factors?

Answer 1

(x - 2i)(x + 2i)(x - 3i)(x = 3i)

Explanation:

`y = x^4 + 13x^2 + 36.`
Call `x^2 = X` and factor this trinomial:
`Y = X^2 + 13X + 36`
Find 2 numbers knowing sum (13) and product (36). They are 4 and 9. Therefor;
Y = (X + 4)(X + 9)
y = (x^2 + 4)(x^2 + 9)
To transform y to linear factors, we can use complex numbers, with i^2 = -1.
y = (x - 2i)(x + 2i)(x - 3i)(x + 3i)