Polynomial factorization question.

[agoogler]

Homework Statement

Factorize :

(x+1) (x+2) (x+3) (x+6)-3 x²

Homework Equations

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The Attempt at a Solution

Expanding everything , I get x⁴+12x³+44x²+72x+36 .
At this point I tried few guesses using rational roots test. But it appears this has no rational roots. So how should I factor this polynomial ?

 

[Filip Larsen]

Perhaps you can utilize that your 4th order polynomial can be written as (x²+ax+b)(x²+cx+d)? (hint: write up the equations relating the unknown a, b, c and d to your polynomial and see if any of those equations makes it easier to make a guess for some of the unknowns).

 

[besulzbach]

= (x + 1) (x + 2) (x + 3) (x + 6) - 3x²
= x⁴ + 12x³ + 44x² + 72x + 36

An educated guess is:

= (x² + ... + 6) (x² + ... + 6)

The missing terms can be found through simple equations involving the coefficients that you obtained when you expanded the initial polynomial.

 

[Filip Larsen]

Besulzbach, please do not provide "complete solutions" in the homework sections. A hint or two that can point the poster in the right direction from where they are stuck is usually better.

 

[besulzbach]

So, should I delete that? I'm used to Yahoo! Answers and here things seem to be different.

 

[Filip Larsen]

So, should I delete that?

Changing your post, as you have also done now, so it only hints the way forward is perfect. :thumbs:

The idea in the homework section of this forum is to help people understand and not to do their homework for them, and providing a full solutions makes it too tempting for people to skip the understanding part, especially if it has to be handed in real soon. Its for the same reason people are asked to show the work they have done up to the point where they are stuck so we know that the poster has put some effort into solving the problem at hand. Greg explains the actual rules in more details under forum menu Site Info / Rules & Guidelines in the section Homework Help Guidelines.