Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I am dealing with an issue for which I do not find answer on the Internet. When I factorize a polynomial, I can get this structure:

$$ (x-a)(x-b)(x-c)^2 $$

But sometimes I have seen others like: $$ k(x-a)(x-b)(x-c)^2 $$

Where $k$ is any real number. What does it mean? I know it is related with the coefficient of the root with the highest algebraic multiplicity but I don't get to understand it.

It could be $\frac{1}{3}(x-1)(x-2)$ but never $(x-1)(x-2)+\frac{1}{3}$ isn't it? Why? Thank you a lot :)

share|improve this question
add comment

1 Answer 1

up vote 2 down vote accepted

$k$ is the leading coefficient, the coefficient of the highest power of the variable. That is, if you expand out $k (x - a)(x-b)(x-c)^2$ you'll get $k x^4 + $ (terms in lower powers of $x$). It has nothing to do with the roots.

On the other hand, $(x-1)(x-2)+\frac{1}{3}$ is not a factorization. To factorize something means to write it as a product of things, not as a product plus something else.

share|improve this answer
    
Thank you a lot. Simple and complete! –  Mark Tower Dec 14 '12 at 8:48
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.