# How do you factor #x^3 - x^2 - 2x + 2=0#?

##### 2 Answers

#### Explanation:

Rewrite the equation

#### Explanation:

#"note that the coefficients "1-1-2+2=0#

#rArr(x-1)" is a factor"#

#"divide the polynomial by "(x-1)#

#color(red)(x^2)(x-1)cancel(color(magenta)(+x^2))cancel(-x^2)-2x+2#

#=color(red)(x^2)(x-1)color(red)(-2)(x-1)cancel(color(magenta)(-2))cancel(+2)#

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

#x^2-2larrcolor(blue)"is a difference of squares"#

#â€¢color(white)(x)a^2-b^2=(a-b)(a+b)#

#"with "a=x" and "b=sqrt2#

#rArrx^2-2=(x-sqrt2)(x+sqrt2)#

#rArrx^3-x^2-2x+2=0#

#rArr(x-1)(x-sqrt2)(x+sqrt2)=0#

#rArrx=1" or "x=+-sqrt2#