What is the quotient of (4x² - 27x + 18) ÷ (x - 6)?

Solution:

Given, (4x² - 27x + 18) ÷ (x - 6)

We have to find the quotient.

By splitting the middle term,

= 4x² - 27x + 18

= 4x² - 24x - 3x + 18

= 4x(x - 6) - 3(x - 6)

= (4x - 3)(x - 6)

Now, (4x² - 27x + 18) ÷ (x - 6) = (4x - 3)(x - 6)/(x - 6)

= 4x - 3

Therefore, the quotient is 4x - 3.

Example:

What is the quotient of (x² + 8x + 12) ÷ (x + 6)?

Solution:

Given, (x² + 8x + 12) ÷ (x + 6)

We have to find the quotient.

By splitting the middle term,

= x² + 8x + 12

= x² + 6x + 2x + 12

= x(x + 6) + 2(x + 6)

= (x + 2)(x + 6)

Now, (x² + 8x + 12) ÷ (x + 6) = (x + 2)(x + 6)/(x + 6)

= x + 2

Therefore, the quotient is x + 2.