a) f(x) = -2x^3 + 7 - 6x + 5x^4 - 2x^3
= 5x^4 - 2x^3 - 2x^3 - 6x + 7
= 5x^4 - 4x^3 - 6x + 7
g(x) = 5x^2 + 9x - 2x^4 - x^2 + 4x^3 -12
= -2x^4 + 4x^3 + 5x^2 - x^2 + 9x - 12
= -2x^4 + 4x^3 + 4x^2 + 9x - 12
b) f(x) + g(x) = (5x^4 - 4x^3 - 6x + 7) + (-2x^4 + 4x^3 + 4x^2 + 9x - 12)
= 5x^4 + (-2x^4) - 4x^3 + 4x^3 + 4x^2 - 6x + 9x + 7 - 12
= 3x^4 + 4x^2 + 3x - 5