Page 41 - Concepts of Reasoning-8

Worksheet-6.2

Division of Algebraic Expressions

1. Write the missing steps in the following problems of dividing a polynomial by another
polynomial.
2
2
x + + 2x + –
3
2
3
2

a. x – 4 x + x – 14x – 24 b. x – 7 2x – 13x – 13x + 42
3
x 3 2x –
– – +
2
5x – 14x – 13x
– 5x 2 – +
– 6x + 42
– + + –
0 0

Quotient = __________ Quotient = __________

Remainder = __________ Remainder = __________

2. Choose the appropriate divisor, quotient and remainder from the following for each of the given
dividend such that the following rule is satisfied :
4
2
2
Divisors = 8x + 6, x – 1, x – 4, 5 – 3x , 3 – x
2
2
5
3
2
2
Quotients = 2x + 7x + 5, 4x + 21x + 27x, –6x + 10x + 24, x + 4x – 12, 5x – 27x – 56
Remainders = 4x + 12, 0, 0, –2x – 1, 1
2
3
a. Dividend = 8x + 38x –72x – 72
Verification of the rule :
Divisor = ____________________ Dividend = (Divisor × Quotient) + Remainder
Quotient = ____________________
Remainder = ____________________
3
2
b. Dividend = 2x – x + 16x + 15
Verification of the rule :
Divisor = ____________________
Dividend = (Divisor × Quotient) + Remainder
Quotient = ____________________
Remainder = ____________________

3
4
2
c. Dividend = –6x + 10x + 30x – 12x – 25
Divisor = ____________________ Verification of the rule :
Dividend = (Divisor × Quotient) + Remainder
Quotient = ____________________
Remainder = ____________________

41 Reasoning - 8