How do you factor #8x^3-12x^2+2x-3#?

1 Answer
Sep 27, 2016

Answer:

#(8x^3-12x+2x-3=color(green)((2x-3)(4x^2+1))#

Explanation:

Notice that the ratio of the coefficients of the terms #8x^3# and #2x#: #8:2=4:1#
is the same as the ratio of the coefficients of the terms #-12x^2# and #-3#: #-12:-3 =4:1#

This hints hat we should group the original expression as
#color(white)("XXX")(color(red)(8x^3+2x))-(color(blue)(12x^2+3))#

#color(white)("XXX")=color(red)(2x(4x^2+1)))-color(blue)(3(4x^2+1))#

then extracting the common factor #(4x^2+1)#
#color(white)("XXX")=(2x-3)(4x^2+1)#

(Note that since #4x^2 >= 0# for #AAx in RR#,
#color(white)("XXX")4x^2+1# can not be equal to #0#
#color(white)("XXX")#and #(4x^2+1)# has no Real factors.