Q. 1 D5.0( 2 Votes )

Find the quotient the and remainder of the following division.

(4x3 – 2x2 + 6x + 7) ÷ (3 + 2x)

Answer :

(4x3 – 2x2 + 6x + 7) ÷ (3 + 2x)


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,


(4x3 – 2x2 + 6x + 7) ÷ (2x + 3)


Now we need to divide (4x3 – 2x2 + 6x + 7) by (2x + 3)


Now we need to find out by how much should we multiple “x” to get a value as much as 4x3.


To get x3, we need to multiply x×x2.


Therefore we need to multiply with 2x2 × (2x + 3) and we get (4x3 + 6x2) now subtract (4x3 + 6x2) from 4x3 – 2x2 + 6x + 7so we get – 8x2.


Now we carry 6x + 7along with 4x2, as shown below


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



here (2x + 3) × (–4x)


= – 8x2 – 12x


here (2x + 3) × 9


= 18x + 27


Therefore, we got the quotient = 2x2 – 4x + 9 and


Remainder = –20


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