How do you factor #6x^3 + 29x^2 + 23x - 30 = 0#?

1 Answer
Oct 3, 2015

Answer:

Technically, you factor #6x^3+29x^2+23x-30# to solve #6x^3+29x^2+23x-30=0#

Step 1: find a linear factor
Step 2: factorise and factorise

Explanation:

#6x^3+29x^2+23x-30=0#

By inspection
#6(-3)^3+29(-3)^2+23(-3)-30#
#=-162+261-69-30=0#

Thus #(x+3)# is a factor

By inspection
#(x+3)(6x^2 + 11x - 10)=0#
#(x+3)(3x - 2)(2x + 5)=0#
#x=-3# or#x=2/3# or #x=-5/2#