How do you factor the expression #12x^3-15x^2-18x#?

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Answer 1 · 2017-01-16T11:22:03

The answer is #=3x(4x+3)(x-2)#

We start by factorising the common factors

#12x^3-15x^2-18x#

#=x(12x^2-15x-18)#

#=3x(4x^2-5x-6)=3x(4x+3)(x-2)#

We compare #4x^2-5x-6# to #ax^2+bx+c#

We calculate

#Delta=b^2-4ac=25+4*24=121#

#x=(-b+-sqrt(Delta))/(2a)#

#x_1=(5+sqrt121)/8=(5+11)/8=2#

#x_2=(5-11)/8=-6/8=-3/4#

Therefore,

#12x^3-15x^2-18x=3x(4)(x-2)(x+3/4)#

#=3x(x-2)(4x+3)#