How do you factor #x^3+x^2-14x-24#?

1 Answer

Answer:

#color(red)(x^3+x^2-14x-24=(x+2)(x+3)(x-4))#

Explanation:

We start from the given 3rd degree polynomial

#x^3+x^2-14x-24#

Use the monomial #-14x#
It is equal to #-4x-10x#

#x^3+x^2-4x-10x-24#

Rearrange

#x^3-4x+x^2-10x-24#

Regroup

#(x^3-4x)+(x^2-10x-24)#

Factoring

#x(x^2-4)+(x+2)(x-12)#

#x(x+2)(x-2)+(x+2)(x-12)#

Factor out the common binomial factor #(x+2)#

#(x+2)[x(x-2)+(x-12)]#

Simplify the expression inside the grouping symbol [ ]

#(x+2)[x^2-2x+x-12]#

#(x+2)(x^2-x-12)#

Factoring the trinomial #x^2-x-12=(x+3)(x-4)#

We now have the factors

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

Final answer

#color(red)(x^3+x^2-14x-24=(x+2)(x+3)(x-4))#

God bless ....I hope the explanation is useful.