Which is a factor of 6x²y + 8x² - 30y - 40?
x - 4, 3y + 4, x² + 4, 3y - 5

Solution:

The given equation is

6x²y + 8x² - 30y - 40

Rearranging the equation we get

= 6x²y - 30y + 8x² - 40

= y(6x² - 30) + 8(x² - 5)

= 6y(x² - 5) + 8(x² - 5)

= (x² - 5)(6y + 8)

= 2(x² - 5)(3y + 4)

Hence the factors of the given equation are:

2, (x² - 5) and (3y + 4)

Another example of identifying factors can be identifying factors of:: 4a² + b² - c² + 4ab

= 4a² + b² - c² + 4ab

= 4a² + 4ab + b² - c²

= (4a² + 4ab + b²) - c²

= (2a + b)² - c² --- (1)

We know that a² - b² = (a + b)(a - b)

In equation (1)

(2a + b)² = a² and c² = b²,

Therefore (1) can be rewritten as (2a + b)² - c² = (2a + b + c)(2a + b - c)

Hence the factors of 4a² + b² - c² + 4ab are (2a + b + c)(2a + b - c)

Which is a factor of 6x²y + 8x² - 30y - 40?
x - 4, 3y + 4, x² + 4, 3y - 5

Summary:

3y + 4 is a factor of 6x²y + 8x² - 30y - 40