How do you factor #x^5+2x^4-x-2#?
1 Answer
May 12, 2016
#x^5+2x^4-x-2=(x-1)(x+1)(x^2+1)(x+2)#
Explanation:
Use the difference of squares identity:
#a^2-b^2 = (a-b)(a+b)#
after factoring by grouping:
#x^5+2x^4-x-2#
#=(x^5+2x^4)-(x+2)#
#=x^4(x+2)-1(x+2)#
#=(x^4-1)(x+2)#
#=((x^2)^2-1^2)(x+2)#
#=(x^2-1)(x^2+1)(x+2)#
#=(x^2-1^2)(x^2+1)(x+2)#
#=(x-1)(x+1)(x^2+1)(x+2)#
