# FINDING QUOTIENT AND REMAINDER USING LONG DIVISION

## About "Finding Quotient and Remainder Using Long Division"

Finding Quotient and Remainder Using Long Division :

Here we are going to see some practice questions on finding quotient and remainder using long division.

## Finding Quotient and Remainder Using Long Division - Practice questions

Question 1 :

Find the quotient and remainder of the following.

(i) (4x3 + 6x2 – 23x +18) ÷ (x + 3)

Solution :

Quotient  =  4x2 - 6x - 5

Remainder  = 33

(ii) (8y3 – 16y2 + 16y –15) ÷ (2y – 1)

Solution :

Quotient  =  4y2 - 6y + 5

Remainder  = -10

(iii) (8x3 – 1) ÷ (2x – 1)

Solution :

Quotient  =  4x2 - 2x - 1

Remainder  = -2

(iv) (-18z + 14z2 + 24z3 + 18) ÷ (3z + 4)

Solution :

=  (-18z + 14z2 + 24z3 + 18) ÷ (3z + 4)

Arrange the given polynomial according to the power.

=  (24z+ 14z2 -18z + 18) ÷ (3z + 4)

Quotient  =  8z2 - 6z + 2

Remainder  = 10

Question 2 :

The area of a rectangle is x2 + 7x + 12. If its breadth is (x + 3), then find its length

Solution :

Area of rectangle  =  length x breadth

x2 + 7x + 12  =  length (x + 3)

Length  =  (x2 + 7x + 12) / (x + 3)

Hence x + 4 is the breadth of the rectangle.

Question 3 :

The base of a parallelogram is (5x + 4). Find its height, if the area is 25x– 16.

Solution :

Area of parallelogram  =  base x height

base  =  5x + 4

Area  =  25x2 - 16

25x2 - 16  =  (5x + 4⋅ height

Height   =   (25x2 - 16) / (5x + 4)

Hence height of the given parallelogram is 5x - 4.

Question 4 :

The sum of (x + 5) observations is (x+ 125). Find the mean of the observations.

Solution :

Sum of (x + 5) observation  =  x+ 125

Total number of observation  =  x + 5

Mean observation  =  (x+ 125)/(x + 5)

After having gone through the stuff given above, we hope that the students would have understood, "Finding Quotient and Remainder Using Long Division"

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