can this be factored?

Question

x^3 - 3x^2 +2

Answer 1

can be factorised to (x-1)(x^2-2x-2)

Answer 2

easy way to find is to use numerical value for x , sustitute and see if the equation goes to zero..then (x-that number) will be a factor
let us use x=1
eqn then simplifies to 1-3+2 =0
so (x-1) wil be a factor
x^3-x^2-2x^2+2x-2x+2
=x^2(x-1)-2x(x-1)-2(x-1)
=(x-1)(x^2-2x-2)
this cannot be factored further
i hope you are aware that ax^2+bx+c cannot be factored if there are no two integers whose product is a*b and the sum is a+b
in this case there are no 2 integers whose product is -2 and the sum of those integers is -2
-2 = -2*+1 but sum =-2+1= -1 not the required -2

Answer 3

let f(x) = x^3-3x^2+2
f(1) = 1-3+2 = 0

so (x-1) is a factor

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

Answer 4

ya... as the sum of coefficients of the given expression is 0, (x-1) is one of the factor. by horners method of synthetic division, we can determine the other factor i.e., (x^2-2x-2) which cannot be resolved into the other factors. so, for the given expression, only two factors are possible.

Answer 5

yes
i can see that x=1 is a zero of this expression
divide it x-1 out and you have a quadratic expression left to factorise.