Algebra 2: Write the polynomial equation of degree 4 with leading coefficient 1 that has roots at -2, -1, 3, and 4. Please help..thank you.?

x = -2 or x = -1 or x = 3 or x = 4
x + 2 = 0 or x + 1 = 0 or x - 3 = 0 or x - 4 = 0
(x + 2)(x + 1)(x - 3)(x - 4) = 0
(x² + 3x + 2)(x² - 7x + 12) = 0
x²(x² - 7x + 12) + 3x(x² - 7x + 12) + 2(x² - 7x + 12) = 0
x⁴ - 7x³ + 12x² + 3x³ - 21x² + 36x + 2x² - 14x + 24 = 0
x⁴ - 4x³ - 7x² + 22x + 24 = 0

[ x + 2 ] [ x + 1 ] [ x - 3 ] [ x - 4 ]
[ x² + 3x + 1 ] [ x² + x + 12 ]

x^4 + x^3 + 12x^2
____3x^3 + 3x^2 + 36x
__________x^2 + x + 12

x^4 + 4x^3 + 16x^2 + 37x + 12 = 0

(x+2)(x+1)(x-3)(x-4)
=(x^2 + 3x + 2)(x^2 -7x +12)

NOw expand it further