Factorization - Jharkhand Board (JAC) STD 8 Maths Questions

Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): The factorisation of $x^2yz + xy^2z + xyz^2$ is $xyz^2(x + y + z).$
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
C
$A$ is true but $R$ is false.
✓
$A$ is false but $R$ is true.

Answer: D.

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Q 7Assertion (A) & Reason (B) MCQ1 Mark

Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): The factorisation of $a^3+a^2 b+a b^2$ is a $\left(a^2+a b+b^2\right)$
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
C
$A$ is true but $R$ is false.
D
$A$ is false but $R$ is true.

Answer: A.

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Q 8Assertion (A) & Reason (B) MCQ1 Mark

Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): The common factor of $7^2 x^3 y^4 z^4, 120 z^2 d^4 x^4$ and $96 y^3 z^4 d^4$ is $72 z^3$
Reasons (R): A common factor is a number that can be divided into two different numbers, without leaving a remainder.

A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
C
$A$ is true but $R$ is false.
✓
$A$ is false but $R$ is true.

Answer: D.

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Q 9Assertion (A) & Reason (B) MCQ1 Mark

Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): The factorisation of $6x + 12y$ is $6 (x + 2y)$
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
C
$A$ is true but $R$ is false.
D
$A$ is false but $R$ is true.

Answer: A.

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Q 10Assertion (A) & Reason (B) MCQ1 Mark

Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): The common factor of $x^3y^2$ and $x^4y$ is $x^3y$.
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.