Question 191268
<pre><font size = 4 color = "indigo"><b>
{{{2p^4+5p^3q+3p^2q^2}}}

First factor out {{{p^2}}}

{{{p^2(2p^2+5pq+3q^2)}}}

In the parentheses, multiply the first coefficient 2
by the last coefficient 3, getting 6.  Write down
all pairs of integer factors whose product is 6.
They are

1*6
2*3

Since the last sign in the parentheses is +, we
add those:

1+6 = 7
2+3 = 5

Since the middle coefficient of {{{(2p^2+5pq+3q^2)}}}
is 5, and since 5 = 2+3 we write 5pq as 2pq+3pq

{{{p^2(2p^2+2pq+3pq+3q^2)}}}

Factor the first two terms in the parentheses by factoring 
out {{{2p}}}

{{{p^2(2p(p+q)+3pq+3q^2)}}}
 
Factor the last two terms in the parentheses by factoring 
out {{{3q}}}

{{{p^2(2p(p+q)+3q(p+q))}}}

Inside the parentheses take out {{{(p+q)}}}

{{{p^2(p+q)(2p+3q)}}}

Edwin</pre>