SOLUTION: factor the following polynomial: x^3+2x^2-x-2

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Question 970657: factor the following polynomial: x^3+2x^2-x-2
Found 4 solutions by Boreal, Fombitz, MathLover1, MathTherapy:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
GROUP THIS
(x^3+2x^2) - (x+2) NOTE: The negative sign distributes across BOTH the x and the 2. This is still the same equation.
Factor both terms:
x^2(x+2) - (1) (x+2) ;l I put in the 1 to emphasize it.
The two (x+2) are each multiplied by something, and that is (x^2-1). I combine them to get (x^2-1) (x+2).
But x^2-1 is a difference of squares, so
(x^2-1) (x+2) becomes (x+1) (x-1)(x+2)

Answer by Fombitz(32388) About Me  (Show Source):
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E3%2B2x%5E2-x-2....write 2x%5E2 as x%5E2%2Bx%5E2 and -x as x-2x
x%5E3%2Bx%5E2%2Bx%5E2%2Bx-2x-2....group
%28x%5E3%2Bx%5E2%29%2B%28x%5E2%2Bx%29-%282x%2B2%29
x%5E2%28x%2B1%29%2Bx%28x%2B1%29-2%28x%2B1%29
%28x%5E2%2Bx-2%29%28x%2B1%29........x as 2x-x
%28x%5E2%2B2x-x-2%29%28x%2B1%29....group
%28%28x%5E2%2B2x%29-%28x%2B2%29%29%28x%2B1%29
%28x%28x%2B2%29-%28x%2B2%29%29%28x%2B1%29
%28x%2B2%29%28x-1%29%28x%2B1%29


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

factor the following polynomial: x^3+2x^2-x-2
x%5E3+%2B+2x%5E2+-+x+-+2

%28x%5E3+%2B+2x%5E2%29+%28-+x+-+2%29 ------- Grouping

x%5E2%28x+%2B+2%29-+1%28x+%2B+2%29

%28x%5E2+-+1%29%28x+%2B+2%29

highlight_green%28%28x+-+1%29%28x+%2B+1%29%28x+%2B+2%29%29 ------ Factoring difference of 2 squares (DOTS)