Finding Quotient and Remainder Using Long Division :
Here we are going to see some practice questions on finding quotient and remainder using long division.
Question 1 :
Find the quotient and remainder of the following.
(i) (4x3 + 6x2 – 23x +18) ÷ (x + 3)
Quotient = 4x2 - 6x - 5
Remainder = 33
(ii) (8y3 – 16y2 + 16y –15) ÷ (2y – 1)
Quotient = 4y2 - 6y + 5
Remainder = -10
(iii) (8x3 – 1) ÷ (2x – 1)
Quotient = 4x2 - 2x - 1
Remainder = -2
(iv) (-18z + 14z2 + 24z3 + 18) ÷ (3z + 4)
= (-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
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.
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.
Sum of (x + 5) observation = x3 + 125
Total number of observation = x + 5
Mean observation = (x3 + 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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