How to Factor Polynomials with Three Terms?

[Hollysmoke]

I'm having trouble with this one factoring problem-

x^2(a+b)-x(a+b)+(a+b)

I thought it was 3 terms so I tried to do decomposition but it doesn't seem to work. If someone could just help me, I'd appreciate it. Thanks!

 

[arildno]

Take out the common factor (a+b) first.

 

[Hollysmoke]

so I'm going to end up (a+b)(x^2-x)?

 

[arildno]

No. If you multiply that out, would you have any constant term?

 

[Hollysmoke]

OH! so (a+b)(x^2-x+1)

 

[arildno]

Quite right!
So, what are the roots of the polynomial hiding inside the brackets?

 

[Hollysmoke]

I'm not sure but its impossible to multiply to -1 and add to 1
1*1=1 and add to 2, 1*-1=-1 but add to 0
so I can't use quadratics...

 

[arildno]

So, you've found that your polynomial hasn't got any real roots, right?
That means your factorization is complete..

 

[Hollysmoke]

Hey hey! Thank you for your help ^_^