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.

How's to make the composition of two polynomials? According to this page:

If $ P = (x^3 + x) $, $ Q = (x^2 + 1) $ then,

$ P\circ Q = P\circ (x^2 + 1) = (x^2 + 1)^3 + (x^2 + 1) = x^6 + 3 x^4 + 4 x^2 + 2 $

It seems that the $ (x^3 + x) $ becomes the $x^3$, then we have $( \space \space \space )^3$ and now we just need to switch the inside of $P$ by the inside of $Q$ thus $(x^2 + 1)^3$.

I'm just not sure if my interpretation is correct. I'm also aware that I may not be using the right terms for describing this, but it's what I have now.

share|improve this question
    
$x^3+x$ doesn't become $x^3$, it stays as $x^3+x$ and then you have $(\ )^3+(\ )$. :) –  Rahul Jul 23 '12 at 15:13
3  
By definition $\: (P\circ Q)(x)\, =\, P(Q(x))\, =\, Q(x)^3 + Q(x)\ \ $ –  Bill Dubuque Jul 23 '12 at 15:39
    
I remember of studying Sum of two polynomials, difference of two polynomials, product of a constant and a polynomial and product of two polynomials. They kinda make sense for me, where is compostion of two polynomials useful? –  Vÿska Jul 23 '12 at 21:30
    
Ah, Another question: Is composition used only on polynomials with two constants? The given examples show me only operations on polynomials such as $(x^3 + x)$ but I've seen no references to polynomials with 3 constants such as $(x^3 + 4x^2 - x)$. –  Vÿska Jul 24 '12 at 4:58

1 Answer 1

up vote 5 down vote accepted

Looks fine. Maybe it becomes even clearer, when you write it like: $$ P\circ Q = (x^3 + x)\circ Q= (Q^3+Q)=(x^2 + 1)^3 + (x^2 + 1) = x^6 + 3 x^4 + 4 x^2 + 2 $$

share|improve this answer
    
You again, Draks? May our friendship last forever, While I'm studying mathematics, I'll ask a lot. Any doubt about our friendship? Axiom 1: There is a friendship between draks and GustavoB such that draks answers GustavoB's noob questions. –  Vÿska Jul 23 '12 at 21:14
1  
@GustavoBandeira Thanks, but don't expect too much, I'm not even a mathematician. The time will come when you answer my questions. Good luck for your studies... –  draks ... Jul 23 '12 at 21:28
    
Well. I can't even sum 2 integers - But I guess I can odd sum 2 integers. You're higher on the hierarchical tree - considering it exists. –  Vÿska Jul 24 '12 at 0:19

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.