How do you factor the expression #6x^3 + 4x^2 + 3x + 2#?

1 Answer
Jan 12, 2016

Answer:

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)#