Find the quotient the and remainder of the following division.

(−18 – 9x + 7x²) ÷ (x – 2)

(−18 – 9x + 7x²) ÷ (x – 2)

We see that the equation is not arranged in descending order, so we need first arrange it in descending order of the power of x.

Therefore it becomes,

(7x² – 9x – 18) ÷ (x – 2)

Now we need to divide (7x² – 9x – 18) by (x – 2).

Now we need to find out by how much should we multiple “x” to get a value as much as 7x².

To get x², we need to multiply x×x.

Therefore, we need to multiply with 7x × (x – 2) and we get (7x² – 14x) now subtract (7x² – 14x) from 7x² – 9x – 18 so we get 5x.

Now we carry 18 along with 5x, as shown below

So, in same way we have keep dividing till we get rid of x as shown below.

here (x – 2) × 5

= 5x – 10

Therefore, we got the quotient = 7x + 5 and

Remainder = – 8