How do you factor completely #x^4 + 5x^2 - 36#?
1 Answer
May 1, 2016
#=(x^2+9)(x-2)(x+2)#
#=(x-3i)(x+3i)(x-2)(x+2)#
Explanation:
Use the difference of squares identity once or twice:
#a^2-b^2 = (a-b)(a+b)#
We can treat this as a quadratic in
#x^4+5x^2-36#
#=(x^2+9)(x^2-4)#
#=(x^2+9)(x^2-2^2)#
#=(x^2+9)(x-2)(x+2)#
The remaining quadratic factor has no linear factors with Real coefficients, but it can also be treated as a difference of squares using
#=(x^2-(3i)^2)(x-2)(x+2)#
#=(x-3i)(x+3i)(x-2)(x+2)#
