How to Factor Polynomials with Three Terms?

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Homework Help Overview

The discussion revolves around factoring a polynomial with three terms, specifically the expression x^2(a+b)-x(a+b)+(a+b). Participants explore different methods of factoring and the implications of their findings regarding the roots of the polynomial.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to use decomposition for factoring but encounters difficulties. Some participants suggest taking out the common factor (a+b) first, leading to further exploration of the resulting expression. Questions arise regarding the roots of the polynomial and the feasibility of using quadratics for factorization.

Discussion Status

The discussion has progressed with participants providing guidance on factoring techniques and exploring the implications of the polynomial's roots. There is acknowledgment that the polynomial does not have real roots, indicating a potential conclusion to the factorization process.

Contextual Notes

Participants are navigating the constraints of the polynomial's structure and the implications of its roots, with some uncertainty about the application of quadratic methods.

Hollysmoke
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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!
 
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Take out the common factor (a+b) first.
 
so I'm going to end up (a+b)(x^2-x)?
 
No. If you multiply that out, would you have any constant term?
 
OH! so (a+b)(x^2-x+1)
 
Quite right!
So, what are the roots of the polynomial hiding inside the brackets?
 
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...
 
So, you've found that your polynomial hasn't got any real roots, right?
That means your factorization is complete..
 
Hey hey! Thank you for your help ^_^
 

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