myhelper: RS Aggarwal solution class 8 chapter 6 Operations on Algebraic Expressions Exercise 6C

Exercise 6C

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Q1 | Ex-6C | Class 8 | RS AGGARWAL | chapter 6 | Operations on Algebraic Expressions | myhelper

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Question 1:

Divide:
(i) 24x²y³ by 3xy
(ii) 36xyz² by −9xz
(iii) −72x²y²z by −12xyz
(iv) −56mnp² by 7mnp

Answer 1:

(i) 24x²y³ by 3xy

$\frac{24 x^{2} y^{3}}{3 x y} \Rightarrow (\frac{24}{3}) (x^{2 - 1}) (y^{3 - 1}) \Rightarrow 8 x y^{2} .$

Therefore, the quotient is 8xy².

(ii) 36xyz² by −9xz

$\frac{36 x y z^{2}}{- 9 x z} \Rightarrow (\frac{36}{- 9}) (x^{1 - 1}) (y^{1 - 0}) (z^{2 - 1}) \Rightarrow - 4 y z$

Therefore, the quotient is −4yz.

(iii)
$- 72 x^{2} y^{2} z b y - 12 x y z \frac{- 72 x^{2} y^{2} z}{- 12 x y z} \Rightarrow (\frac{- 72}{- 12}) (x^{2 - 1}) (y^{2 - 1}) (z^{1 - 1}) \Rightarrow 6 x y$

Therefore, the quotient is 6xy.

(iv) −56mnp² by 7mnp

$\frac{- 56 m n p^{2}}{7 m n p} \Rightarrow (\frac{- 56}{7}) (m^{1 - 1}) (n^{1 - 1}) (p^{2 - 1}) \Rightarrow - 8 p$

Therefore, the quotient is −8p.

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Question 2:

Divide:
(i) 5m³− 30m² + 45m by 5m
(ii) 8x²y² − 6xy² + 10x²y³ by 2xy
(iii) 9x²y − 6xy + 12xy² by − 3xy
(iv) 12x⁴ + 8x³ − 6x² by − 2x²

Answer 2:

(i) 5m³− 30m² + 45m by 5m

$(5 m^{3} - 30 m^{2} + 45 m) \div 5 m \Rightarrow \frac{5 m^{3}}{5 m} - \frac{30 m^{2}}{5 m} + \frac{45 m}{5 m} \Rightarrow m^{2} - 6 m + 9$

Therefore, the quotient is m² − 6m + 9.

(ii) 8x²y² − 6xy² + 10x²y³ by 2xy

$(8 x^{2} y^{2} - 6 x y^{2} + 10 x^{2} y^{3}) \div 2 x y \Rightarrow \frac{8 x^{2} y^{2}}{2 x y} - \frac{6 x y^{2}}{2 x y} + \frac{10 x^{2} y^{3}}{2 x y} \Rightarrow 4 x y - 3 y + 5 x y^{2}$

Therefore, the quotient is 4xy − 3y + 5xy².

(iii) 9x²y − 6xy + 12xy² by − 3xy

$(9 x^{2} y - 6 x y + 12 x y^{2}) \div - 3 x y \Rightarrow \frac{9 x^{2} y}{- 3 x y} - \frac{6 x y}{- 3 x y} + \frac{12 x y^{2}}{- 3 x y} \Rightarrow - 3 x + 2 - 4 y$

Therefore, the quotient is −3x + 2 − 4y.

(iv) 12x⁴ + 8x³ − 6x² by − 2x²

^{$(12 x^{4} + 8 x^{3} - 6 x^{2}) \div - 2 x^{2} \Rightarrow \frac{12 x^{4}}{- 2 x^{2}} + \frac{8 x^{3}}{- 2 x^{2}} - \frac{6 x^{2}}{- 2 x^{2}} \Rightarrow - 6 x$ ²-4x+3²}

Therefore the quotient is −6x² − 4x + 3.

Q3 | Ex-6C | Class 8 | RS AGGARWAL | chapter 6 | Operations on Algebraic Expressions | myhelper

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Question 3:

Write the quotient and remainder when we divide:
(x² − 4x + 4) by (x − 2)

Answer 3:

Therefore, the quotient is $(x - 2)$ and the remainder is 0.

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Question 4:

Write the quotient and remainder when we divide:
(x² − 4) by (x + 2)

Answer 4:

Therefore, the quotient is $x$ −2 and the remainder is 0.

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Question 5:

Write the quotient and remainder when we divide:
(x² + 12x + 35) by (x + 7)

Answer 5:

(x² + 12x + 35) by (x + 7)

Therefore, the quotient is $(x + 5)$ and the remainder is 0.

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Question 6:

Write the quotient and remainder when we divide:
(15x² + x − 6) by (3x + 2)

Answer 6:

Therefore, the quotient is $(5 x - 3)$ and the remainder is 0.

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Question 7:

Write the quotient and remainder when we divide:
(14x² − 53x + 45) by (7x − 9)

Answer 7:

Therefore, the quotient is $(2 x - 5)$ and the remainder is 0.

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Question 8:

Write the quotient and remainder when we divide:
(6x² − 31x + 47) by (2x − 5)

Answer 8:

Therefore, the quotient is $(3 x - 8)$ and the remainder is 7.

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Question 9:

Write the quotient and remainder when we divide:
(2x³ + x² − 5x − 2) by (2x + 3)

Answer 9:

Therefore, the quotient is $(x^{2} - x - 1)$ and the remainder is 1.

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Question 10:

Write the quotient and remainder when we divide:
(x³ + 1) by (x + 1)

Answer 10:

Therefore, the quotient is $x^{2}$ -x+1 and the remainder is 0.

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Question 11:

Write the quotient and remainder when we divide:
(x⁴ − 2x³ + 2x² + x + 4) by (x² + x + 1)

Answer 11:

Therefore, the quotient is ( x² - 3x + 4) and remainder is 0.

Q12 | Ex-6C | Class 8 | RS AGGARWAL | chapter 6 | Operations on Algebraic Expressions | myhelper

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Question 12:

Write the quotient and remainder when we divide:
(x³ − 6x² + 11x − 6) by (x² − 5x + 6)

Answer 12:

Therefore, the quotient is (x-1) and the remainder is 0.

Q13 | Ex-6C | Class 8 | RS AGGARWAL | chapter 6 | Operations on Algebraic Expressions | myhelper

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Question 13:

Write the quotient and remainder when we divide:
(5x³ − 12x² + 12x + 13) by (x² − 3x + 4)

Answer 13:

Therefore, the quotient is ( 5x+ 3) and the remainder is (x + 1).

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Question 14:

Write the quotient and remainder when we divide:
(2x³ − 5x² + 8x − 5) by (2x² − 3x + 5)

Answer 14:

Therefore, the quotient is (x-1) and the remainder is 0.

Q15 | Ex-6C | Class 8 | RS AGGARWAL | chapter 6 | Operations on Algebraic Expressions | myhelper

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Question 15:

Write the quotient and remainder when we divide:
(8x⁴ + 10x³ − 5x² − 4x + 1) by (2x² + x − 1)

Answer 15:

Therefore, the quotient is ( 4x²+ 3x -2) and the remainder is ( x-1).

RS Aggarwal solution class 8 chapter 6 Operations on Algebraic Expressions Exercise 6C

Exercise 6C

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Q1 | Ex-6C | Class 8 | RS AGGARWAL | chapter 6 | Operations on Algebraic Expressions | myhelper

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