How do you factor #x^3+6x^2-5x-30#?

2 Answers
Apr 15, 2018

Answer:

#x= -6, x= ##+-##sqrt#5

Explanation:

rearrange the equation
#x^3 - 5x + 6x^2 - 30#

take out the common factors
#x(x^2 -5) +6(x^2 - 5)#

compress the terms
#(x+6)(x^2 - 5)#

solve for #x#
#x= -6, x= ##+-##sqrt#5

Apr 15, 2018

Answer:

#(x+6)(x-sqrt5)(x+sqrt5)#

Explanation:

#color(blue)"factor by grouping the terms"#

#=color(red)(x^2)(x+6)color(red)(-5)(x+6)#

#"take out the "color(blue)"common factor "(x+6)#

#=(x+6)(color(red)(x^2-5))#

#x^2-5" can be factored using "color(blue)"difference of squares"#

#a^2-b^2=(a-b)(a+b)#

#x^2-5=x^2-(sqrt5)^2#

#"with "a=x" and "b=sqrt5#

#rArrx^2-5=(x-sqrt5)(x+sqrt5)#

#rArrx^3+6x^2-5x-30=(x+6)(x-sqrt5)(x+sqrt5)#