# 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)#