SOLUTION: factor the polynomial by grouping 2p^4+5p^3q+3p^2q^2

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Question 191268: factor the polynomial by grouping
2p^4+5p^3q+3p^2q^2
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

2p%5E4%2B5p%5E3q%2B3p%5E2q%5E2

First factor out p%5E2

p%5E2%282p%5E2%2B5pq%2B3q%5E2%29

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 %282p%5E2%2B5pq%2B3q%5E2%29
is 5, and since 5 = 2+3 we write 5pq as 2pq+3pq

p%5E2%282p%5E2%2B2pq%2B3pq%2B3q%5E2%29

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

p%5E2%282p%28p%2Bq%29%2B3pq%2B3q%5E2%29
 
Factor the last two terms in the parentheses by factoring 
out 3q

p%5E2%282p%28p%2Bq%29%2B3q%28p%2Bq%29%29

Inside the parentheses take out %28p%2Bq%29

p%5E2%28p%2Bq%29%282p%2B3q%29

Edwin