FINDING QUOTIENT AND REMAINDER USING LONG DIVISION

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.

 =  (24z³ + 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 25x² – 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 (x³ + 125). Find the mean of the observations.

Solution :

Sum of (x + 5) observation  =  x³ + 125

Total number of observation  =  x + 5

Mean observation  =  (x³ + 125)/(x + 5)

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