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 :

$Q=(4x^2-27x+18)\div(x-6)=\dfrac{4x^2-27x+18}{x-6}~~~~~~~~~~~~~~~~~~~~~~~(i)$

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

$Q\\\\\\=\dfrac{4x^2-27x+18}{x-6}\\\\\\=\dfrac{4x^2-24x-3x+18}{x-6}\\\\\\=\dfrac{4x(x-6)-3(x-6)}{x-6}\\\\\\=\dfrac{(x-6)(4x-3)}{(x-6)}\\\\=4x-3.$

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