I'm not sure how to title this but here's the problem;
Define $a,b,c$ so that $P(x) + Q(x) = 0$ with every value of $x$.
$P(x) = 5x^2 - ax + 4 - (bx^2 - 7x + 3)$ and $Q(x) = 8x^2 + x + c$.
So you need to find values for $a, b$ and $c$ which will make the sum of $P(x)$ and $Q(x)$ equal to zero, no matter what you will input as the value of $x$.
I've tried simplifying the sum of the polynomials but that's how far I'll get. I can deduce the correct answer by trying different values but i don't think it's how you are supposed to solve this problem.
How you should mathematically approach this problem? Can you create an equation out of this?