How do you write #x^4 + 13x^2 + 36# as a product of linear factors?
1 Answer
Apr 9, 2016
(x - 2i)(x + 2i)(x - 3i)(x = 3i)
Explanation:
Call
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)