Splitting a polynomial into sum of factors, not necessarily linear

How can I split a given polynomial as sum of factors in Mathematica?

For example, let's say I have this polynomial: $2\cdot x^2+7\cdot x+2$.

I would like the output to be $(x+1)(x+2)+x(x+4)$. Is there a way to do that with Mathematica?

• What you want is not really factorization, because that's about multiplication of factors. There's an infinity of terms that can be added to arrive at the same result. But have a look at Factor anyway. Mar 31 '15 at 6:15
• 'Factor' doesn't give a possible way to write factors as sum of products. Apr 7 '15 at 6:04

expr = 2 x^2 + 7 x + 2;