How do you factor the expression x^3-3*x+2?

Question

Please help me!

359 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-23T13:05:59

#x^3-3x+2=(x-1)^2(x+2)#

If sum of the coefficients of an algebraic polynomial #f(x)# is #0#, then #x-1# a factor of #f(x)#

This is because then #f(1)=0# and hence according to factor theorem #x-1# is a factor of #f(x)#.

Here coefficients are #1,-3,2# and as their sum is #0#, #x-1# is a factor of #x^3-3x+2#. Now dividing #x^3-3x+2# by #x-1#, we get

#x^3-3x+2#

= #x^2(x-1)+x(x-1)-2(x-1)#

= #(x-1)(x^2+x-2)#

= #(x-1)(x^2+2x-x-2)#

= #(x-1)(x(x+2)-1(x+2))#

= #(x-1)(x-1)(x+2)#

= #(x-1)^2(x+2)#

Observe that sum of the coefficients of #x^2+x-2# too is #0# i.e. #x-1# is a factor of #x^2+x-2# too.