Let's solve this problem by representing the three consecutive even numbers as x, x + 2, and x + 4.

According to the given information, the sum of these numbers is 270:

x + (x + 2) + (x + 4) = 270

Combining like terms, we have:

3x + 6 = 270

Subtracting 6 from both sides:

3x = 264

Dividing both sides by 3:

x = 88

Therefore, the three consecutive even numbers are 88, 90, and 92.

(6x^2 – 25x – 10) ÷ (3x + 2)
= (6x^2/3x + 2) + (-25x/3x + 2) + (-10/3x + 2)
= 2x - 29/3 R. 28/3

To simplify the given polynomial, combine like terms:

cd^2 + 6a^2c^2 - 8cd^2 + a^2c^2

Combine the terms with the same variables:

(cd^2 - 8cd^2) + (6a^2c^2 + a^2c^2)

Combine the coefficients:

-7cd^2 + 7a^2c^2

So, the simplified polynomial is -7cd^2 + 7a^2c^2.

4x^6(-10x^5 + 4)
= (4x^6)(-10x^5) + (4x^6)(4)
= 16x^6 - 40x^11