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CBSE Questions for Class 8 Maths Factorisation Quiz 1 - MCQExams.com
CBSE
Class 8 Maths
Factorisation
Quiz 1
Evaluate
$$(x^3 + 2x^2 + 3x) \div 2x$$
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$$(x^2 + 2x - 3) \div 2$$
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$$(x^2 - 2x + 3) \div 2$$
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$$(x^2 + 2x + 3) \div 2$$
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$$(x^2 + x + 3) \div 2$$
Explanation
$$(x^3+2x^2+3x)\div 2x$$
$$=(x\times x\times x)+(2\times x\times x)+(3\times x)$$
$$=\frac{x(x^2+2x+3)}{2x}$$
$$=\frac{1}{2}(x^2+2x+3)$$
Factorise:
$$16a^2-24ab$$
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$$8 (2a -3b)$$
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$$8a (2a +3b)$$
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$$8a (2a -3b)$$
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$$8a (2a -3)$$
Explanation
$$16a^2-24ab$$
Taking 8a as a common,
$$=8a(2a-3b)$$
Answer $$8a(2a-3b)$$
The process of finding the factors of given number (or expression) is called ...........
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multiplication
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factorisation
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division
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addition
Explanation
The process of finding the factors of given number (or expression) is called Factorization.
Evaluate
$$(10x - 25) \div 5$$
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$$2x-5$$
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$$2x+6$$
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$$3x-5$$
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$$3x+6$$
Explanation
$$(10 x - 25) \div 5 $$
$$= \displaystyle \frac{10 x - 25}{5}$$
$$ = \dfrac{5 \times (2x - 5)}{5} $$
$$= 2x - 5$$
Factorise the following expression:
$$7a^2 + 14a$$
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$$7a(a + 2)$$
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$$7(a - 2)$$
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$$14(7a + 1)$$
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$$7a(a - 2)$$
Explanation
Given expression is $$7a^2 + 14a$$
Taking common factor $$7a$$ from both terms we get,
$$7a(a+2)$$
Hence, option A is correct.
Factorise the following expressions:
$$a x^2 y + b x y^2 + c x y z$$
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xy(ax + by + cz)
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axy(x + by + cz)
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bxy(ax + y + cz)
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xy(ax + by - cz)
Explanation
$$a x^2 y + b x y^2 + c x y z$$
In the above expression, the common factor is $$=xy$$
$$\therefore$$
$$a x^2 y + b x y^2 + c x y z $$
= $$xy(ax+by+cz)$$
Factorise the expression:
$$ax^2 + bx$$
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$$x(ax + b)$$
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$$x(ax - b)$$
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$$x(a + b)$$
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$$x(a - b)$$
Explanation
To factorise: $$ax^2+bx$$
Now,
$$ax^2+bx$$
$$=ax\times x+b\times x$$
$$=x(ax+b)$$
Hence, the factorised form is $$x(ax+b)$$ .
Factorise the following expression:
$$ 16 z + 20 z^3$$
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$$4z( 2 - 5z^2)$$
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$$4z( 4 + 5z)$$
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$$4z( 4 + 5z^2)$$
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$$4z( 2 + 5z^2)$$
Explanation
$$16 z + 20 z^3$$
Taking common factor 4z from both the terms we get,
$$=4z(4+5z^2)$$
Factorise the following expression:
$$ 4 a^2 + 4 ab -4 ca$$
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$$4a( a + b - c)$$
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$$4b( a + b - c)$$
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$$4c( a + b - c)$$
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$$4a(a+b+c)$$
Explanation
$$4a^{ 2 }+4ab-4ca$$
The common factor $$=2\times 2\times a$$
Thus, $$4a^{ 2 }+4ab-4ca=4a(a+b-c)$$
Factorise the following expressions.
$$20l^2 m + 30 a l m = 10lm(2l+3a)$$
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True
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False
Explanation
$$20 { l}^{2 } m + 30 a l m$$
$$=10lm(2l+3a)$$
Factorize:
$$5 x^2 y -15 xy^2$$
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$$5x(x-3y)$$
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$$3x(x-5y)$$
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$$5xy(x-3y)$$
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$$3xy(x-5y)$$
Explanation
$$5{x }^{ 2}y-15x{y}^{2}$$
Taking common factor $$5xy$$ for both the terms we get,
$$=5xy(x-3y)$$
Factorise the expression.
$$7p^2 + 21q^2$$
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$$7(p^2 + 7q^2)$$
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$$7(p^2 + 2q^2)$$
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$$7(p^2 + 3q^2)$$
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$$7(p^2 + 4q^2)$$
Explanation
$$\begin{aligned}{}7{p^2} + 21{q^2}& = 7{p^2} + 7 \times 3{q^2}\\ &= 7\left( {{p^2} + 3{q^2}} \right)\end{aligned}$$
Divide the given polynomial by the given monomial.
$$(3y^8- 4y^6 + 5y^4) \div y^4$$
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$$3y^4 +4y^2 + 5$$
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$$3y^4 -4y^2 + 5$$
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$$3y^4 -2y^2 + 5$$
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$$3y^4 +2y^2 + 5$$
Explanation
$$(3y^{ 8 }-4y^{ 6 }+5y^{ 4 })\div y^{ 4 }$$
$$=\dfrac{(3y^{ 8 }-4y^{ 6 }+5y^{ 4 })}{y^{ 4 }}$$
$$=\dfrac{y^4(3y^{ 4 }-4y^{ 2 }+5)}{y^{ 4 }}$$
$$=(3y^{ 4 }-4y^{ 2 }+5)$$
Divide the given polynomial by the given monomial.
$$(x^3 + 2x^2 + 3x)\div 2x$$
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$$\dfrac{1}{2}(x^2+2x+3)$$
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$$\dfrac{1}{4}(x^2-2x+3)$$
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$$\dfrac{1}{2}(x^2-2x+3)$$
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$$\dfrac{1}{2}(x^2+2x-3)$$
Explanation
$$(x^{ 3 }+2x^{ 2 }+3x)\div 2x$$
$$=\dfrac{(x^{ 3 }+2x^{ 2 }+3x)}{2x}$$
$$=\dfrac{x(x^2+2x+3)}{2x}$$
$$=\dfrac{(x^2+2x+3)}{2}$$
Divide the given polynomial by the given monomial.
$$8(x^3y^2z^2 + x^2y^3z^2 + x^2y^2z^3)\div 4x^2y^2z^2$$
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$$2(x - y + z)$$
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$$2(x + y-z)$$
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$$2(x + y + z)$$
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$$4(x + y + z)$$
Explanation
$$8(x^{ 3 }y^{ 2 }z^{ 2 }+x^{ 2 }y^{ 3 }z^{ 2 }+x^{ 2 }y^{ 2 }z^{ 3 })\div 4x^{ 2 }y^{ 2 }z^{ 2 }$$
$$=\dfrac{8(x^{ 3 }y^{ 2 }z^{ 2 }+x^{ 2 }y^{ 3 }z^{ 2 }+x^{ 2 }y^{ 2 }z^{ 3 })}{4x^{ 2 }y^{ 2 }z^{ 2 }}$$
$$=\dfrac{8x^2y^2z^2(x+y+z)}{4x^{ 2 }y^{ 2 }z^{ 2 }}$$
$$=2(x+y+z)$$
Factorize
$$3a^{2}-9ab$$ by taking common factors.
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$$3a\left ( a-3b \right )$$
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$$3a\left ( a-b \right )$$
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$$3a\left ( 3a-b \right )$$
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$$3a\left ( a+b \right )$$
Explanation
$$3a^{2}-9ab$$
$$3$$ and $$a$$ are common in the above two terms in the addition, so taking these as common.
$$3a^2-9ab=3a(a-3b)$$
Option A is correct.
Factorise: $$5t+25t^2$$
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$$5t(1+5t)$$
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$$t(1-5t)$$
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$$5t(1-5t)$$
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$$t(1+5t)$$
Explanation
$$5t+25t^2$$
$$=5t(1+5t)$$
Factorise: $$ab-4ac$$
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$$a(b+ 4c)$$
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$$(b- 4c)$$
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$$a(b- 4c)$$
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$$a(b- c)$$
Explanation
The common variable in the two terms is $$a$$. So, we can take $$a$$ common from both the terms as follows:
$$ ab-4ac =a(b-4c)$$
Hence, option C is correct.
Factorise:
$$4a + 12b$$
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$$4(a + 3b)$$
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$$a(4+3b)$$
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$$4a(1+3b)$$
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$$4(a+4b)$$
Explanation
$$4a+12b$$
$$= (2\times 2 \times a) + (2\times 2\times 3 \times b)$$
$$= (2\times 2) (a + 3 \times b)$$
$$= 4 (a+3b)$$
Factorise
$$a^3 - a^2 + a$$
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$$a(a^2 - a - 1)$$
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$$a(a^2 + a + 1)$$
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$$(a^2 - a + 1)$$
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$$a(a^2 - a + 1)$$
Factorise: $$4x-8y$$
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$$4(x-4y)$$
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$$3(x-y)$$
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$$4(3x-2y)$$
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$$4(x-2y)$$
Explanation
$$4x-8y$$
$$=4(x-2y)$$
Factorise
$$15 x + 5$$
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$$5(3x + 1)$$
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$$5(x+1)$$
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$$3(5x+1)$$
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$$15(x+1)$$
Explanation
$$ 15x+5$$
$$= (5\times 3 \times x) + (5\times1)$$
$$= 5(3\times x +1) $$
$$= 5(3x+1)$$
Factorise $$9b-12x$$
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$$2(3b + 4x)$$
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$$3(b - 4x)$$
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$$3(3b - 4x)$$
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$$2(3b - x)$$
Explanation
$$Factorizing\quad 9b-12x,\\ 3*\frac { 9b-12x }{ 3 } \quad =3(3b-4x)$$
State whether True or False.
Divide: $$ -4a^2b^3-8ab^2+6ab$$ by $$-2ab $$ , then answer is $$2ab^2+4b-3$$.
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True
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False
Explanation
$$\Rightarrow \frac{-4a^2b^3-8ab^2+6ab}{-2ab}$$
In $$-4a^2b^3-8ab^2+6ab$$we take $$-2ab$$ common then
$$\Rightarrow \frac{-2ab\left(2ab^2+4b-3 \right)}{-2ab}$$
$$\Rightarrow 2ab^2+4b-3$$
State whether True or False.
Divide: $$ 15a^3b^4- 10a^4b^3-25a^3b^6 $$ by $$ -5a^3b^2 $$, then answer is $$-3b^2+2ab+5b^4$$.
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True
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False
Explanation
$$\Rightarrow 15a^3b^4- 10a^4b^3-25a^3b^6 \div -5a^3b^2 $$
$$\Rightarrow \frac{15a^3b^4- 10a^4b^3-25a^3b^6}{-5a^3b^2}$$
we take $$5a^3b^2$$common
$$\Rightarrow \frac{5a^3b^2\left (3b^2-2ab-5b^4 \right )}{-5a^3b^2}$$
$$\Rightarrow -3b^2+2ab+5b^4 $$
Factorise
$$4a^2 - 8 ab$$
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$$4a(a + 2b)$$
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$$4a(a - b)$$
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$$4a(a - 2b)$$
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$$a(a - 2b)$$
Explanation
Given expression is $$4a^2-8ab$$.
Taking $$4a$$ common from both terms of $$4a^2-8ab$$, we get:
$$4a(a-2b)$$
Hence, $$4a^2-8ab=4a(a-2b)$$.
Factorise:
$$3x^2 + 6x^3$$
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$$3x^2 (1 + 2x)$$
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$$3x^2 (1 - 2x)$$
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$$x^2 (1 + 2x)$$
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$$3x^2 (1 + x)$$
Explanation
$$Factorizing:\quad { 3x }^{ 2 }+{ 6x }^{ 3 },\\ we\quad take\quad 3{ x }^{ 2 }\quad common,\\ =3{ x }^{ 2 }(1+2x)$$
State whether True or False.
Factorization of $$6x^3 - 8x^2$$ is $$2x^2 (3x - 4)$$.
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True
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False
Explanation
$$\\ 6{ x }^{ 2 }+8{ x }^{ 3 }\\ =2{ x }^{ 2 }(3-4x)\\ \\ $$
State whether True or False
Factorization of $$36 x^2 y^2 - 30 x^3 y^3 + 48 x^3 y^2$$ is $$6x^2 y^2 (6 - 5xy + 8x)$$.
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True
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False
Explanation
$$Factorizing\quad 36x^{ 2 }y^{ 2 }-30x^{ 3 }y^{ 3 }+48x^{ 3 }y^{ 2 },\\ =6x^{ 2 }y^{ 2 }(6-5xy+8x)$$
State whether True or False.
Divide: $$ -14x^6y^3-21x^4y^5+7x^5y^4 $$ by $$ 7x^2y^2$$, then answer is $$-2x^4y-3x^2y^3+x^3y^2$$.
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True
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False
Explanation
$$\Rightarrow -14x^6y^3-21x^4y^5+7x^5y^4 \div 7x^2y^2$$
$$\Rightarrow \frac{-14x^6y^3-21x^4y^5+7x^5y^4}{7x^2y^2}$$
We take $$7x^2y^2$$common
$$\Rightarrow \frac{7x^2y^2\left (-2x^4y-3x^2y^3+x^3y^2 \right )}{7x^2y^2}$$
$$\Rightarrow -2x^4y-3x^2y^3+x^3y^2$$
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