Question

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

Answer 1

I'll use synthetic division: (you can also use long division or factoring)

6 | 4 -27 18
| 24 -18
__________
4 -3 0

So the quotient is 4x-3

Answer 2

Answer: The required quotient of the given division is (4x - 3).

Step-by-step explanation: We are given to find the following quotient :

`Q=(4x^2-27x+18)/(x-6)=(4x^2-27x+18)/(x-6)~~~~~~~~~~~~~~~~~~~~~~~(i)`

To find the given quotient, first we need to factorize the numerator and then we will try to divide it by the denominator.

From (i), we have

`Q\\\\\\=(4x^2-27x+18)/(x-6)\\\\\\=(4x^2-24x-3x+18)/(x-6)\\\\\\=(4x(x-6)-3(x-6))/(x-6)\\\\\\=((x-6)(4x-3))/((x-6))\\\\=4x-3.`

Thus, the required quotient of the given division is (4x - 3).