How do you factor #x^5+x^3+8x^2+8#?
1 Answer
Nov 16, 2015
Factor by grouping and the sum of cubes identity to find:
#x^5+x^3+8x^2+8 = (x^2+1)(x+2)(x^2-2x+4)#
Explanation:
The sum of cubes identity may be written:
#a^3+b^3=(a+b)(a^2-ab+b^2)#
We use this with
#x^5+x^3+8x^2+8#
#=(x^5+x^3)+(8x^2+8)#
#=(x^2+1)x^3 + (x^2+1)8#
#=(x^2+1)(x^3+8)#
#=(x^2+1)(x^3+2^3)#
#=(x^2+1)(x+2)(x^2-x(2)+2^2)#
#=(x^2+1)(x+2)(x^2-2x+4)#
