Question 1162286
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The factorization is going to be of the form<br>
{{{(ax+by+c)(dx+ey+f)}}}<br>
You could expand that expression to obtain a large number of equations in several variables....  But you don't want to do that.<br>
Use logical reasoning instead.<br>
(1) To get the 2x^2 term in the product, you need an "x" and a "2x":<br>
(x+???)(2x+???)<br>
(2) To get the 3y^2 term in the product, you need a "y" and a "3y".  There are two possibilities:<br>
(x+y+???)(2x+3y+???)
or
(x+3y+???)(2x+y+???)<br>
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<br>
(x+3y+???)(2x+y+???)<br>
To get the constant term 4 in the product, we have three possibilities:<br>
(x+3y+1)(2x+y+4)  --  gives terms of 6x and 13y, which are both wrong<br>
(x+3y+2)(2x+y+2)  --  gives terms of 6x and 8y, which are both wrong<br>
(x+3y+4)(2x+y+1)  --  gives us terms of 9x and 7y, which are correct<br>
ANSWER: (x+3y+4)(2x+y+1)<br>