CBSE Class 8 Mathematics Algebraic Expressions and Factorisation MCQs Set 13

Multiple Choice Questions (MCQs) for Class 8 Mathematics: Algebraic Expressions and Factorisation

Explore reliable objective questions for Algebraic Expressions and Factorisation tailored for Class 8 learners. Utilizing these Mathematics multiple-choice formats ensures thorough preparation and strengthens problem-solving speed for upcoming school assessments.

Practice Algebraic Expressions and Factorisation MCQs for Class 8 Mathematics

Access the complete set of multiple-choice questions for Algebraic Expressions and Factorisation below. This focused format allows students to isolate specific topics for thorough review and uninterrupted practice alongside official CBSE textbooks.

Multiple Choice Questions

Question 1: If x and y are non-zero unequal rational numbers, \( \frac{(x+y)^2-(x-y)^2}{x^2y-xy^2} \) equals:
(a) \( \frac{2}{x-y} \)
(b) \( \frac{1}{xy} \)
(c) \( \frac{4}{x-y} \)
(d) \( \frac{1}{x-y} \)
Show Answer & Explanation

Answer: (c) \( \frac{4}{x-y} \)

Explanation:
1. Numerator = 4xy (since (x + y)^2 - (x - y)^2 = 4xy).
2. Denominator = xy(x - y), so the value is 4/(x - y).

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

Question 2: If (x - 2) is a factor of \( x^2+3qx-2q \), then q equals:
(a) \( -1 \)
(b) \( -2 \)
(c) \( 2 \)
(d) \( 1 \)
Show Answer & Explanation

Answer: (a) \( -1 \)

Explanation:
1. Put x = 2: 4 + 6q - 2q = 0.
2. 4q = -4, so q = -1.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Question 3: If \( x^3+6x^2+4x+k \) is exactly divisible by (x + 2), then k equals:
(a) \( -8 \)
(b) \( 8 \)
(c) \( -4 \)
(d) \( 4 \)
Show Answer & Explanation

Answer: (a) \( -8 \)

Explanation:
1. Put x = -2: -8 + 24 - 8 + k = 0.
2. k = -8.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Question 4: Let \( f(x)=x^3-6x^2+11x-6 \). Which of the following is not a factor of f(x)?
(a) \( x-2 \)
(b) \( x-3 \)
(c) \( x-1 \)
(d) \( x+3 \)
Show Answer & Explanation

Answer: (d) \( x+3 \)

Explanation:
1. f(1) = 0, f(2) = 0 and f(3) = 0, so x - 1, x - 2 and x - 3 are factors (f(x) = (x - 1)(x - 2)(x - 3)).
2. f(-3) = -27 - 54 - 33 - 6 is not zero, so x + 3 is not a factor.

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

Question 5: \( x^{29}-x^{25}+x^{13}-1 \) is divisible by:
(a) both (x - 1) and (x + 1)
(b) (x + 1) but not by (x - 1)
(c) neither (x - 1) nor (x + 1)
(d) (x - 1) but not by (x + 1)
Show Answer & Explanation

Answer: (d) (x - 1) but not by (x + 1)

Explanation:
1. At x = 1: 1 - 1 + 1 - 1 = 0, so (x - 1) is a factor.
2. At x = -1: -1 + 1 - 1 - 1 = -2, not zero, so (x + 1) is not a factor.

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

Question 6: The value of k for which (x - 1) is a factor of \( x^3-k \) is:
(a) \( -1 \)
(b) \( 0 \)
(c) \( 2 \)
(d) \( 1 \)
Show Answer & Explanation

Answer: (d) \( 1 \)

Explanation:
1. Put x = 1: 1 - k = 0, so k = 1.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Question 7: Find the factors of \( 8x^3-27y^3 \).
(a) \( (2 x - 3 y)(4 x^{2} - 6 x y + 9 y^{2}) \)
(b) \( (2 x - 3 y)(4 x^{2} + 6 x y + 9 y^{2}) \)
(c) \( (- 2 x - 3 y)(4 x^{2} + 6 x y + 9 y^{2}) \)
(d) \( (2 x + 3 y)(4 x^{2} + 6 x y + 9 y^{2}) \)
Show Answer & Explanation

Answer: (b) \( (2 x - 3 y)(4 x^{2} + 6 x y + 9 y^{2}) \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( (2 x - 3 y)(4 x^{2} + 6 x y + 9 y^{2}) \).

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

Question 8: Find the factors of \( x^3+y^3+2x^2-2y^2 \).
(a) \( (x + y)(x^{2} + x y + 2 x + y^{2} - 2 y) \)
(b) \( (- x + y)(x^{2} - x y + 2 x + y^{2} - 2 y) \)
(c) \( (x + y)(x^{2} - x y + 2 x + y^{2} - 2 y) \)
(d) \( (x - y)(x^{2} - x y + 2 x + y^{2} - 2 y) \)
Show Answer & Explanation

Answer: (c) \( (x + y)(x^{2} - x y + 2 x + y^{2} - 2 y) \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( (x + y)(x^{2} - x y + 2 x + y^{2} - 2 y) \).

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

Question 9: Find the factors of \( x^3-5x^2+8x-4 \).
(a) \( (x - 1)(x - 2)^{2} \)
(b) \( (- x - 1)(x - 2)^{2} \)
(c) \( (x - 1)(- x - 2)^{2} \)
(d) \( (x + 1)(x - 2)^{2} \)
Show Answer & Explanation

Answer: (a) \( (x - 1)(x - 2)^{2} \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( (x - 1)(x - 2)^{2} \).

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

Question 10: Find the factors of \( x^4+4 \).
(a) \( (x^{2} - 2 x + 2)(x^{2} - 2 x + 2) \)
(b) \( (x^{2} - 2 x - 2)(x^{2} + 2 x + 2) \)
(c) \( (x^{2} + 2 x + 2)(x^{2} + 2 x + 2) \)
(d) \( (x^{2} - 2 x + 2)(x^{2} + 2 x + 2) \)
Show Answer & Explanation

Answer: (d) \( (x^{2} - 2 x + 2)(x^{2} + 2 x + 2) \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( (x^{2} - 2 x + 2)(x^{2} + 2 x + 2) \).

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

Question 11: When \( x^5-9x^2+12x-14 \) is divided by (x - 3), the remainder is:
(a) \( 170 \)
(b) \( 184 \)
(c) \( 198 \)
(d) \( -184 \)
Show Answer & Explanation

Answer: (b) \( 184 \)

Explanation:
1. Remainder = value at x = 3: 243 - 81 + 36 - 14.
2. = 184.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Question 12: When \( x^{11}+1 \) is divided by (x + 1), the remainder is:
(a) \( 0 \)
(b) \( 2 \)
(c) \( -2 \)
(d) \( 1 \)
Show Answer & Explanation

Answer: (a) \( 0 \)

Explanation:
1. Value at x = -1: (-1)^11 + 1 = 0.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Question 13: The value of \( 16x^2+24x+9 \) for x = -3/4 is:
(a) \( 0 \)
(b) \( 9 \)
(c) \( 18 \)
(d) \( 1 \)
Show Answer & Explanation

Answer: (a) \( 0 \)

Explanation:
1. 16x^2 + 24x + 9 = (4x + 3)^2.
2. At x = -3/4: 4x + 3 = 0, so the value is 0.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Question 14: The sum of \( x^2+1 \) and the reciprocal of \( x^2-1 \) is:
(a) \( \frac{x^4+1}{x^2-1} \)
(b) \( \frac{x^4}{x^2-1} \)
(c) \( \frac{x^4}{x^2+1} \)
(d) \( \frac{2x^2}{x^2-1} \)
Show Answer & Explanation

Answer: (b) \( \frac{x^4}{x^2-1} \)

Explanation:
1. Sum = (x^2 + 1) + 1/(x^2 - 1) = ((x^2 + 1)(x^2 - 1) + 1)/(x^2 - 1).
2. = (x^4 - 1 + 1)/(x^2 - 1) = x^4/(x^2 - 1).

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

Question 15: Find the factors of \( x^2-1-2a-a^2 \).
(a) \( (- a + x - 1)(a + x + 1) \)
(b) \( (- a + x - 1)(a - x + 1) \)
(c) \( (a + x - 1)(a + x + 1) \)
(d) \( (- a + x + 1)(a + x + 1) \)
Show Answer & Explanation

Answer: (a) \( (- a + x - 1)(a + x + 1) \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( (- a + x - 1)(a + x + 1) \).

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

Question 16: Find the factors of \( x^2-xy-72y^2 \).
(a) \( (- x - 9 y)(x + 8 y) \)
(b) \( (x - 9 y)(x - 8 y) \)
(c) \( (x - 9 y)(x + 8 y) \)
(d) \( (x + 9 y)(x + 8 y) \)
Show Answer & Explanation

Answer: (c) \( (x - 9 y)(x + 8 y) \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( (x - 9 y)(x + 8 y) \).

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

Question 17: Find the factors of \( x^2-11xy-60y^2 \).
(a) \( (x - 15 y)(x - 4 y) \)
(b) \( (- x - 15 y)(x + 4 y) \)
(c) \( (x + 15 y)(x + 4 y) \)
(d) \( (x - 15 y)(x + 4 y) \)
Show Answer & Explanation

Answer: (d) \( (x - 15 y)(x + 4 y) \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( (x - 15 y)(x + 4 y) \).

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

Question 18: Find the factors of \( x^4+x^2+25 \).
(a) \( (x^{2} + 3 x + 5)(x^{2} + 3 x + 5) \)
(b) \( (x^{2} - 3 x + 5)(x^{2} + 3 x + 5) \)
(c) \( (x^{2} - 3 x - 5)(x^{2} + 3 x + 5) \)
(d) \( (x^{2} - 3 x + 5)(x^{2} - 3 x + 5) \)
Show Answer & Explanation

Answer: (b) \( (x^{2} - 3 x + 5)(x^{2} + 3 x + 5) \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( (x^{2} - 3 x + 5)(x^{2} + 3 x + 5) \).

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

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Algebraic Expressions and Factorisation Objective Questions & Solutions for Class 8 Mathematics

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FAQs

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