Factoring Polynomials: Help for a Mathematically Challenged Young Man

[ForwardDrift]

Hey,

This isn't really a homework question, per se, as I am relearning some pre calculus for kicks. But I figured his would be the place to ask. For whatever reason, this very simply factoring issue has got my head spinning. I'm not exactly sure what I am doing wrong to factor this equation completely.

Homework Statement

[(x-1)(x+2)² - (x-1)²(x+2)]

Homework Equations

n/a

The Attempt at a Solution

So here is what I did (though I am sure incorrectly) so far. I have not clue what to do after that.

[(x-1)(x+2)² - (x-1)²(x+2)]

[(x-1)(x+2)(x-2) - (x-1)(x-1)(x+2)]

And then ?Anyway, I'm utterly lost in this simply problem, please help a mathematically challenged young man. Thanks-ForwardDrift

 

[SammyS]

Hey,

This isn't really a homework question, per se, as I am relearning some pre calculus for kicks. But I figured his would be the place to ask. For whatever reason, this very simply factoring issue has got my head spinning. I'm not exactly sure what I am doing wrong to factor this equation completely.

Homework Statement

[(x-1)(x+2)² - (x-1)²(x+2)]

Homework Equations

n/a

The Attempt at a Solution

So here is what I did (though I am sure incorrectly) so far. I have not clue what to do after that.

[(x-1)(x+2)² - (x-1)²(x+2)]

[(x-1)(x+2)(x-2) - (x-1)(x-1)(x+2)]

And then ?

Anyway, I'm utterly lost in this simply problem, please help a mathematically challenged young man. Thanks - ForwardDrift

Hello ForwardDrift. Welcome to PF !

What factor(s) is(are) common to (x-1)(x+2)(x-2) and (x-1)(x-1)(x+2) ?

Factor it (them) out.

Whatever remains should be combined.

 

[ForwardDrift]

Thanks, I'm glad to be on physics forum SammyS!

Note: I realized the second (x-2) in my post should have been a (x+2), instead...

So this is what I ended up doing...

(x-1)(x+2)(x+2) - (x-1)(x-1)(x+2)

(x+2)(x-1) [ (x - 1) - ( x + 2) ]

(x+2)(x-1) [ 3]

3(x+2)(x-1)Is this right, Sammy? I'm not sure about that 3. Something seems wrong about the way I calculated the inside brackets. Am I supposed to reverse a (-) or (+) inside the brackets or something?

-ForwardDrift

 

[SammyS]

Thanks, I'm glad to be on physics forum SammyS!

Note: I realized the second (x-2) in my post should have been a (x+2), instead...

So this is what I ended up doing...

(x-1)(x+2)(x+2) - (x-1)(x-1)(x+2)

(x+2)(x-1) [ (x - 1) - ( x + 2) ]

(x+2)(x-1) [ 3]

3(x+2)(x-1)


Is this right, Sammy? I'm not sure about that 3. Something seems wrong about the way I calculated the inside brackets. Am I supposed to reverse a (-) or (+) inside the brackets or something?

-ForwardDrift

Not quite.

[ (x - 1) - ( x + 2) ] = [ x - 1 -x -2 ] = -3

 

[ForwardDrift]

Alright, thanks Sam, my man. You have been a great help! :)