Factor: 4x5y2 - 10x2y2 - 16x3y.?

1)
4x^5y^2 * 10x^2y^2 - 16x^3y
= 2(2x^5y^2 - 5x^2y^2 - 8x^3y)
= 2x^2y(2x^3y - 5y - 8x)

2)
(2a^2 - a + 6) - (a^2 - 2a + 1)
= 2a^2 - a + 6 - a^2 + 2a - 1
= 2a^2 - a^2 - a + 2a + 6 - 1
= a^2 + a + 5

3)
(x^3 + 5x^2 - 2x - 24)/(x + 4)

....................x^2 + x - 6
......._________________
x + 4)x^3 + 5x^2 - 2x - 24
........x^3 + 4x^2
-------------------------------------
...................x^2 - 2x
..................x^2 + 4x
-------------------------------------
.........................-6x - 24
.........................-6x - 24
-------------------------------------

(x^3 + 5x^2 - 2x - 24)/(x + 4)
= x^2 - x - 6
= x^2 + 2x - 3x - 6
= (x^2 + 2x) - (3x + 6)
= x(x + 2) - 3(x + 2)
= (x + 2)(x - 3)

I do believ it would be 2(2)(2)(5)xy - 2(2)(2)(5)xy-2(2)(2)(2)(3)xy

Shoot me if I'm wrong. :)

Assuming that you mean :-

4 x^5 y² - 10x² y² - 16x³ y
2 x² y (2 x³ y - 5y - 8x)