9514 1404 393
Answer:
(x +3)(x -3)(x +2i)(x -2i)
Step-by-step explanation:
The factoring to quadratics makes use of the fact that -36 = (-9)(4).
x^4 -5x^2 -36
= x^4 -9x^2 +4x^2 -36
= x^2(x^2 -9) +4(x^2 -9)
= (x^2 +4)(x^2 -9)
The form for factoring the difference of squares comes into play here. Of course -4 = (2i)^2.
= (x^2 -(2i)^2)(x^2 -3^2)
= (x -2i)(x +2i)(x -3)(x +3) . . . factored to linear terms
