For what real values of c is 4x^2 + 14x + c - 2x^2 - 10x the square of a binomial?
Simplify first.
\(4x^2 + 14x +c -2x^2 - 10x = 2x^2 + 4x + c\).
If this is a square of a binomial, its discriminant is zero.
\(4^2 - 4(2)(c) = 0 \\ 8c = 16\\ c = 2\)
Check: The resulting polynomial 2x^2 + 4x + 2 is indeed the square of the binomial \((\sqrt 2 x + \sqrt 2)^2\)
