How do you factor the expression #6x^3 + 4x^2 + 3x + 2#?
1 Answer
Jan 12, 2016
Factor by grouping to find:
#6x^3+4x^2+3x+2#
#=(2x^2+1)(3x+2)#
#=(sqrt(2)x-i)(sqrt(2)x+i)(3x+2)#
Explanation:
Factor by grouping:
#6x^3+4x^2+3x+2#
#=(6x^3+4x^2)+(3x+2)#
#=2x^2(3x+2) + 1(3x+2)#
#=(2x^2+1)(3x+2)#
The remaining quadratic factor has no linear factors with Real coefficients, but can be factored as a difference of squares using Complex coefficients:
#=((sqrt(2)x)^2-i^2)(3x+2)#
#=(sqrt(2)x-i)(sqrt(2)x+i)(3x+2)#
