The given polynomials are \(\displaystyle{5}{x}-{2}\) and \(\displaystyle{3}{x}+{4}\)

We have to subtract the polynomials using the horizontal format.

Subtract \(\displaystyle{5}{x}-{2}\) from \(\displaystyle{3}{x}+{4}\)

\(\displaystyle{\left({3}{x}+{4}\right)}-{\left({5}{x}-{2}\right)}={3}{x}+{4}-{\left({5}{x}\right)}-{\left(-{2}\right)}\)

\(\displaystyle={3}{x}+{4}-{5}{x}+{2}\)

\(\displaystyle={\left({3}{x}-{5}{x}\right)}+{\left({4}+{2}\right)}\)

\(\displaystyle={\left(-{2}{x}\right)}+{\left({6}\right)}\)

\(\displaystyle=-{2}{x}+{6}\)

Answer: After subtracting \(5x−2\) from \(3x+4\) the resultant polynomial is \(−2x+6\).