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This mock test of Test: Factorisation- 1 for Class 8 helps you for every Class 8 entrance exam.
This contains 20 Multiple Choice Questions for Class 8 Test: Factorisation- 1 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

Divide as directed: 5 (2x + 1) (3x + 5) ÷ (2x + 1)

Solution:

∴ 5(2x + 1)(3x + 5) (2x + 1) = 5(3x+5)

QUESTION: 2

Divide as directed: 26xy (x + 5) (y – 4) ÷ 13x (y – 4)

Solution:

26*xy*(*x* + 5) (*y* - 4) / 13*x*(*y* - 4)

Cancelling 13x(y-4)

=2y(x+5)

QUESTION: 3

Find and correct the errors in the following mathematical statements. 4 (x – 5) = 4x – 5

Solution:

By the distributive property a(b-c)=ab- ac

so 4(x-5)=4x-20

QUESTION: 4

Find and correct the errors in the following mathematical statements.

x (3x + 2) = 3x^{2} + 2

Solution:

x (3x + 2)= 3x^{2}+2x (by distributive property a(b+c)=ab+ac)

QUESTION: 5

Factorise: 10x^{2 }− 18x^{3 }+ 14x^{4}

Solution:

10x^{2} − 18x^{3 }+ 14x^{4 }= 2x(5x− 9x^{2} + 7x^{3}) = 2x^{2}(5− 9x + 7x^{2})

QUESTION: 6

Factorise: x^{2}+xy+ 8x+ 8y

Solution:

x^2 + xy + 8x + 8y = x[x + y] + 8[x + y]

= (x + y)(x + 8)

QUESTION: 7

Factorise: 4y^{2 }−12y + 9

Solution:

We have 4y^{2 }- 12y+9. comparing the equation with (a-b)^{2}=a^{2}-2ab+b^{2},gives us a^{2}=(2y)^{2},2ab=2*3*2y and b^{2}=(3)^{2}.Hence the answer is (2y-3)^{2}.

QUESTION: 8

Solve: 7x^{2}y^{2}z^{2 }÷ 14xyz

Solution:

7x²y²z²÷14xyz

=(7/14)(x²/x)(y²/y)(z²/z)

=1/2(x)(y)(z)

=1/2xyz.

QUESTION: 9

Find the common factors of 2y, 22xy.

Solution:

Only 2y is common in both the terms

QUESTION: 10

The _______ may be numbers, algebraic variables or algebraic expressions.

Solution:

Factors are numbers we can multiply together to get another number. A constituent or element that brings about certain effects or results, or indicates a specific multiple, number, or quantity.

QUESTION: 11

Factorise : x^{4} - (y+z)^{4}

Solution:

x^{4}- (y+z)^{4}, applying x^{2 }- y^{2}=(x-a)(x+a), gives (x^{2}-(y+z)^{2})(x^{2}+(y+z)^{2}). Again applying the same identity gives (x-(y+z))(x+(y+z))(x^{2}+(y+z)^{2})

QUESTION: 12

Factorise: x^{4}− (x−z)^{4}

Solution:

x^{4}-(x-z)^{4 }= (x^{2}-(x-z)^{2})(x^{2}+(x-z)^{2}) = (x-(x-z))(x+(x-z)(x^{2}+(x-z)^{2}) = z(2x-z)(x^{2}+(x-z)^{2}(Applying a^{2 }- b^{2 }= (a+b)(a-b))

QUESTION: 13

Divide the given polynomial by the given monominal: 8 (x^{3}y^{2}z^{2} + x^{2}y^{3}z^{2} + x^{2}y^{2}z^{3}) ÷ 4x^{2}y^{2}z^{2}

Solution:

8 (x^{3}y^{2}z^{2} + x^{2}y^{3}z^{2} + x^{2}y^{2}z^{3}) ÷ 4x^{2}y^{2}z^{2}

=

QUESTION: 14

Divide the given polynomial by the given monomial: (x^{3}+ 2x^{2}+ 3x) ÷ 2x

Solution:

(x^{3}+2x^{2}+3x)/2x

=x(x^{2}+2x+3)/2x

=(x^{2}+2x+3)/2

QUESTION: 15

Divide as directed: 52pqr (p + q) (q + r) (r + p) ÷104pq (q + r) (r + p)

Solution:

QUESTION: 16

Divide as directed: 20 (y+ 4) (y^{2}+ 5y+ 3) ÷ 5(y+ 4)

Solution:

QUESTION: 17

Find and correct the errors in the following mathematical statements. 2x + 3y = 5xy

Solution:

LHS = 2*x* + 3*y*

RHS = 5*xy*

LHS ≠ RHS

Correct statement would be

2*x* + 3*y* = 2x+3y

QUESTION: 18

Find and correct the errors in the following mathematical statements. x + 2x + 3x = 5x

Solution:

x+2x+3x=6x

QUESTION: 19

Factorise: 12x + 36

Solution:

Let us take 12 as common

and then the factor is 12(x+3) .

QUESTION: 20

Factorise: 15xy – 6x + 5y – 2

Solution:

15xy - 6x + 5y - 2 = 3x[5y-2] + 1[5y-2]

= (5y - 2)(3x + 1)

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