SOLUTION: how to factorize 2x^2+7xy+3y^2+9x+7y+4 Please please help me with this question Thanks in advance

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Question 1162286: how to factorize 2x^2+7xy+3y^2+9x+7y+4
Please please help me with this question
Thanks in advance
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52817) (Show Source):
You can put this solution on YOUR website!
.

= (x + 3y + 4)*(2x + y + 1).

Answer by greenestamps(13203) (Show Source):
You can put this solution on YOUR website!

The factorization is going to be of the form

You could expand that expression to obtain a large number of equations in several variables.... But you don't want to do that.

Use logical reasoning instead.

(1) To get the 2x^2 term in the product, you need an "x" and a "2x":

(x+???)(2x+???)

(2) To get the 3y^2 term in the product, you need a "y" and a "3y". There are two possibilities:

(x+y+???)(2x+3y+???)
or
(x+3y+???)(2x+y+???)

The first possibility will give a term 5xy, which is not what we need; the second gives a term 7xy, which is what we want. So the factorization is

(x+3y+???)(2x+y+???)

To get the constant term 4 in the product, we have three possibilities:

(x+3y+1)(2x+y+4) -- gives terms of 6x and 13y, which are both wrong

(x+3y+2)(2x+y+2) -- gives terms of 6x and 8y, which are both wrong

(x+3y+4)(2x+y+1) -- gives us terms of 9x and 7y, which are correct

ANSWER: (x+3y+4)(2x+y+1)