Factorisation Test

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Factorisation Test - 12

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Weekly Quiz Competition

Question 1
1 / -0

Factorize by taking out the common factors:
$$3a^{2}\, -\, 9ab$$

A
$$3a (a - 3b)$$

B
$$3a (a + 3b)$$

C
$$2a (a - 3b)$$

D
$$2a (a + 3b)$$

Solution

$$3a^2-9ab$$
$$=3a(a-3b)$$
Question 2
1 / -0

Factorise $$6p -12q$$

A
$$(p-2q)$$

B
$$6(p-2q)$$

C
$$6(p-q)$$

D
$$(p-q)$$

Solution

$$6p-12q$$
$$=2\times3\times p-2\times 2\times3\times q$$
$$=2\times3(p-2q)$$
$$=6(p-2q)$$
Question 3
1 / -0

Factorise $$-16z + 20z^3$$

A
$$-z (4 - 5z^3) $$

B
$$-z (4 - 5z^2) $$

C
$$4z (4 - 5z^2) $$

D
$$-4z (4 - 5z^2) $$

Solution

$$-16z+20z^3$$
$$=-4\times 4\times z+4\times 5\times z\times z\times z$$
$$=4z(5z^2-4)$$
Question 4
1 / -0

Factorize : $$y^2 + 100y$$

A
$$y(y+100)$$

B
$$y^2(y+100)$$

C
$$y(y^2+100)$$

D
none of these

Solution

We need to find value of $$y^2+100y$$
Taking $$y$$ common, we get $$y(y+100)$$.
Hence, option A is correct.
Question 5
1 / -0

Factorise :
$$4x+12$$

A
$$4(x+2)$$

B
$$4(x+3)$$

C
$$3(x+4)$$

D
none of these

Solution

$$4x+12=4(x+3)$$
Question 6
1 / -0

Factorise: $$20l^2m + 30alm$$

A
$$10 l m ( 2l +3a)$$

B
$$10 l m ( l +3a)$$

C
$$20 l m ( 2l +3a)$$

D
$$30 l m ( 2l +a)$$

Solution

We have, $$20l^2 m =2 \times 2 \times 5 \times l \times l \times m$$
and, $$30alm = 3 \times 2 \times 5 \times a \times l \times m $$
The two terms have $$ 2, 5, l$$ and $$m$$ as common factors
$$\therefore 20l^2m + 30alm = (2 \times 2 \times 5 \times l \times l \times m)+ (3 \times 2 \times 5 \times a \times l \times m) =2 \times 5 \times l \times m \times (2 \times l \times +3 \times a) $$
$$= 10lm (2l + 3a)$$
Question 7
1 / -0

Factorise: $$7x - 42$$

A
$$7x$$

B
$$x-7$$

C
$$7$$

D
$$7(x-6)$$

Solution

$$7x-42$$
$$=7(x-6)$$
Question 8
1 / -0

Factorise $$x^2yz + xy^2z + xyz^2$$

A
$$yz(x+y-z)$$

B
$$xyz(x-y+z)$$

C
$$xyz(x+y+z)$$

D
$$xyz(2x+y+2z)$$

Solution

Take $$xyz$$ common from every term,

$$x^2yz+xy^2z+xyz^2=xyz(x+y+z)$$
Question 9
1 / -0

Factorise: $$7a^2 +14a$$

A
$$7a (a + 2)$$

B
$$14a (a + 1)$$

C
$$7a (a - 2)$$

D
$$14 (a + 2)$$

Solution

Take $$7a$$ common from the given expression.
$$7a^{2}+14a$$ $$=7a(a+2)$$
Question 10
1 / -0

Factorise $$5x^2y -15xy^2$$

A
$$2xy ( 2x - 15y )$$

B
$$5y ( x - 15y )$$

C
$$5xy ( x - 3y )$$

D
$$xy (5 x - 3y )$$

Solution

$$5x^2y-15xy^2$$
$$=5\times x\times x\times y-5\times 3\times x\times y\times y$$
$$=5xy(x-3y)$$

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Factorisation Test - 12

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Factorisation Test - 12

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Question 1

$$3a (a - 3b)$$

$$3a (a + 3b)$$

$$2a (a - 3b)$$

$$2a (a + 3b)$$

Solution

Question 2

$$(p-2q)$$

$$6(p-2q)$$

$$6(p-q)$$

$$(p-q)$$

Solution

Question 3

$$-z (4 - 5z^3) $$

$$-z (4 - 5z^2) $$

$$4z (4 - 5z^2) $$

$$-4z (4 - 5z^2) $$

Solution

Question 4

$$y(y+100)$$

$$y^2(y+100)$$

$$y(y^2+100)$$

none of these

Solution

Question 5

$$4(x+2)$$

$$4(x+3)$$

$$3(x+4)$$

none of these

Solution

Question 6

$$10 l m ( 2l +3a)$$

$$10 l m ( l +3a)$$

$$20 l m ( 2l +3a)$$

$$30 l m ( 2l +a)$$

Solution

Question 7

$$7x$$

$$x-7$$

$$7$$

$$7(x-6)$$

Solution

Question 8

$$yz(x+y-z)$$

$$xyz(x-y+z)$$

$$xyz(x+y+z)$$

$$xyz(2x+y+2z)$$

Solution

Question 9

$$7a (a + 2)$$

$$14a (a + 1)$$

$$7a (a - 2)$$

$$14 (a + 2)$$

Solution

Question 10

$$2xy ( 2x - 15y )$$

$$5y ( x - 15y )$$

$$5xy ( x - 3y )$$

$$xy (5 x - 3y )$$

Solution

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