Factor the four-term polynomial.

pq - 2r + pr - 2q.

I don't understand how to do it, being stuck under a truckload of summer school work because I moved and missed valuable material. Walk throughs are preferable.

Question

Factor the four-term polynomial.

pq - 2r + pr - 2q.

I don't understand how to do it, being stuck under a truckload of summer school work because I moved and missed valuable material. Walk throughs are preferable.

mathmale · Answer

You might have to experiment to factor this.  The trick is to identify the terms that have something in common and to group them.  
suggestion:  leave the 1st and 4th terms where they are, and interchange the 2nd and 3rd terms.  Write out your result here.

anonymous · Answer

Pq - pr + 2r - 2q?

Or do the signs not retain placement? @mathmale

mathmale · Answer

Each term retains (keeps) its sign.

mathmale · Answer

Thus, pq - 2r + pr - 2q becomes pq + pr - 2r - 2q

mathmale · Answer

Agree or disagree?

anonymous · Answer

Agree, it seems easier in correlation to the signs etc as well.

mathmale · Answer

Now interchange the first 2 terms.

anonymous · Answer

So. Pr + pq - 2r - 2q?

mathmale · Answer

Now which letter do the first 2 terms have in common?  which numeral have the 2nd 2 terms in common?

mathmale · Answer

After you've answered those questions, go ahead and factor the 1st 2 terms and then factor the right 2 terms.

anonymous · Answer

Well that's p, and 2 respectively, but I'm not even sure how to factor becaus dive lost so much school time.

mathmale · Answer

Well, the first two terms both have p in them, don't they?

anonymous · Answer

Yes

mathmale · Answer

Then the first two terms of  Pr + pq - 2r - 2q          factor to p(r+q).
Please factor the second two terms.      - 2r - 2q   factor to ...   ?

anonymous · Answer

Q + 2?

mathmale · Answer

Please look at  - 2r - 2q and identify what it is (what factor) the two terms have in common.

anonymous · Answer

- 2

mathmale · Answer

Right.   So, factor out that -2.  rewrite   - 2r - 2q in factored form.

anonymous · Answer

(q-r)?

mathmale · Answer

What happened to the -2?  You have to keep it.

mathmale · Answer

You've correctly identified -2 as a factor.  What's left, after you've divided   - 2r - 2q  by -2?

mathmale · Answer

- 2r - 2q
----------  =  ?
         -2

anonymous · Answer

Wouldn't it just be 1r -  1q?

mathmale · Answer

- 2r - 2q factors as follows:  -2(r+q).
Make certain you understand this before we move on.

mathmale · Answer

Pr + pq - 2r - 2q
can be re-written as p(r+q) + what?

mathmale · Answer

OpenStudy says you are now offline.  Please, next time, would you tell me you're leaving?
We had this problem almost done.