Simplify $4x-(3x-2)$. A student computed $4x-3x-2$ and concluded the answer is $x-2$. Evaluate the student's work and pick the correct conclusion.

Simplify $(4x^2+6x)+(-x^2+2x)$ and factor the result by pulling out the greatest common factor.

A student simplified $5x^2+3x-(2x^2-4x+1)$ and wrote $3x^2-x+1$. Identify whether the student made an error, and if so, provide the correct simplification.

Simplify the sum of three polynomials: $(2x^2+x-3)+(-x^2+4x+5)+(x^2-6x-2)$.

Simplify and evaluate the polynomial $(2x^2-3x+5)+(-x^2+4x-2)$ at $x=2$.