How do you Factor completely #2x^3+5x^2-37x-60#?

2 Answers
Jul 15, 2018

#(x-4)(x+5)(2x+3)#

Explanation:

Note that #x=4# is a solution
#2*4^3+5*4^2-37*4-60=128+80-148-60=0#
and

#x=-5#

#-2*5^3+5*25+37*5-60=-250+125+185-60=0#
so we can

#2*x^3+5*x^2-37*x-60#
divide by #(x-4)(x+5)#
and we get #2x+3#
so the completely factorization is given by

#(x-4)(x+5)(2x+3)#

Jul 15, 2018

#(x-4)(x+5)(2x+3)#

Explanation:

#2x^3+5x^2-37x-60#

=#2x^3-8x^2+13x^2-52x+15x-60#

=#2x^2*(x-4)+13x*(x-4)+15*(x-4)#

=#(x-4)*(2x^2+13x+15)#

=#(x-4)*(2x^2+10x+3x+15)#

=#(x-4)((2x*(x+5)+3*(x+5))#

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