Question 217217

{{{4x^3-24x^2-x+6}}} Start with the given expression



{{{(4x^3-24x^2)+(-x+6)}}} Group like terms



{{{4x^2(x-6)-1(x-6)}}} Factor out the GCF {{{4x^2}}} out of the first group. Factor out the GCF {{{-1}}} out of the second group



{{{(4x^2-1)(x-6)}}} Since we have the common term {{{x-6}}}, we can combine like terms



{{{(2x+1)(2x-1)(x-6)}}} Factor {{{4x^2-1}}} using the difference of squares to get {{{(2x+1)(2x-1)}}}



So {{{4x^3-24x^2-x+6}}} factors to {{{(2x+1)(2x-1)(x-6)}}}



In other words, {{{4x^3-24x^2-x+6=(2x+1)*(2x-1)*(x-6)}}}