# Find linear polynomials satisfying an identity

Find $$a,b,c,d,e,f,g,h \in \mathbb{R}$$ such that

$$(x+2y+3)(ax+by+cz+d) + (y+z+2)(ex+fy+gz+h) + x+y+z = (ax+by+cz+d)(ex+fy+gz+h)$$

holds in $$\mathbb{R}[x,y,z]$$.

Is there a $$$$good$$"$$ way for this? Or is there a calculator or afunction in Wolfram Mathematica that can do this automatically?

Any help appreciated!

• Simplest way, compare coefficients of $x$, $y$ and $z$ and constant terms on both sides and proceed. – Akash Patalwanshi Mar 30 at 3:47