To add the polynomials, combine the like terms.

(2x² + 3x - 4) + (x² - x + 5)

2x² + x² + 3x - x - 4 + 5

Combine the like terms:

3x² + 2x + 1

Note that the polynomial x² - 9 is in the difference of squares form:

x² - 9 = (x - 3)(x + 3)

To factor the polynomial x³ - 8, use the 'difference of cubes' formula:

a³ - b³ = (a - b)(a² + ab + b²)

where a = x and b = 2:

x³ - 8 = (x - 2)(x² + 2x + 4)

To multiply the polynomial by a constant, multiply each term by the constant:

-3(2x² - 5x + 4)

Distribute the constant:

-6x² + 15x - 12

To solve the equation, first factor the quadratic:

x² - 6x + 9 = (x - 3)(x - 3)

Set the factors equal to 0:

(x - 3)(x - 3) = 0

x - 3 = 0 → x = 3

Since both factors are the same, there is only one solution: x = 3.