Can #y=x^3-3x^2-10x # be factored? If so what are the factors ?

3 Answers
Jul 11, 2017

Answer:

#y=x(x-5)(x+2)#

Explanation:

Take x out as a factor first to give:

#y=x(x^2-3x-10)#

Then factorise the quadratic in the brackets to give the answer above.

Jul 11, 2017

Answer:

#y=x(x-5)(x+2)#

Explanation:

Inspection reveals that all three terms have #x# common in the given polynomial
#y=x^3-3x^2-10x# .....(1)

LHS can be written as
#x(x^2-3x-10)#

The quadratic in the brackets can be factorized by splitting the middle term
#(x^2-3x-10)#
#=>(x^2-5x+2x-10)#
#=>(x[x-5]+2[x-5])#
#=>([x-5][x+2])#

Hence factors are

#y=x(x-5)(x+2)#

Jul 12, 2017

Answer:

#y = x(x-5)(x+2)#

Explanation:

Take out the common factor of #x# first:

#y = x^3 -3x^2 -10x#

#y = x(x^2-3x-10)#

To factorise the quadratic trinomial, find factors of #10# which subtract to give #3#

#15xx2 = 10 and 5-2 =3# so these are the factors we need.

Their signs must be different, but there must be more negatives.
This gives:

#y = x(x-5)(x+2)#