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

##### 3 Answers

#### Explanation:

#"factor the terms "color(blue)"by grouping"#

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

#"take out the "color(blue)"common factor "(x-2)#

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

#x^2+1" can be factored using "color(blue)"difference of squares"#

#a^2-b^2=(a-b)(a+b)#

#"with "a=x" and "b=ito(i=sqrt-1)#

#=(x-2)(x+i)(x-i)larrcolor(red)"in factored form"#

#### Explanation:

or

and bringing the common factor

solving the equation for

solving the equation for

graph{x^3-2x^2+x-2 [-10, 10, -5, 5]}

#### Explanation:

We will use a factoring method called grouping. If we group the first and the third and the second and the fourth together, each grout has its own greatest common factor:

Now we see another CF between the two terms :