Factorisation Test

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Factorisation Test - 21

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Weekly Quiz Competition

Question 1
1 / -0

Divide $$\displaystyle \left( 24x-42 \right)$$ by $$\left( 4x-7 \right) $$

A
$$\displaystyle 4x-7$$

B
$$\displaystyle 3$$

C
$$\displaystyle 6$$

D
$$\displaystyle 7$$

Solution

$$\displaystyle \left( 24x-42 \right) \div \left( 4x-7 \right) =\frac { 24x-42 }{ 4x-7 } $$

$$\displaystyle =\frac { 6\left( 4x-7 \right) }{ 4x-7 } =6$$
Question 2
1 / -0

Factorise: $$\displaystyle 13{ x }^{ 2 }y-65x{ y }^{ 2 }$$

A
$$\displaystyle xy(x-y)$$

B
$$\displaystyle 65xy(x-y)$$

C
$$\displaystyle 13xy(x-5y)$$

D
$$\displaystyle 13xy(x-y)$$

Solution

$$\displaystyle 13{ x }^{ 2 }y-65x{ y }^{ 2 }=\left( 13\times x\times x\times y \right) -\left( 13\times y\times x\times y\times y \right) \\ $$
$$\displaystyle =13xy\left( x-5y \right) $$
Question 3
1 / -0

Factorisation of the expression $$\displaystyle -15x+5{ x }^{ 3 }$$ gives result as

A
$$\displaystyle 5x( 3-{ x }^{ 2 }) $$

B
$$\displaystyle 5x( { x }^{ 2 }-3) $$

C
$$\displaystyle -5x( { x }^{ 2 }-3 ) $$

D
$$\displaystyle x( { x }^{ 2 }-3) $$

Solution

$$\displaystyle -15x+5{ x }^{ 3 }=\left( -5\times 3\times x \right) +\left( 5\times x\times x\times x \right) $$
$$\displaystyle = -5x( 3-{ x }^{ 2 }) $$
$$\displaystyle = 5x ( { x }^{ 2 }-3) $$
Question 4
1 / -0

Find the factors of $$3x^{2} - 3x - 90$$.

A
$$(x + 6)(x - 5)$$

B
$$3(x - 6)(x + 5)$$

C
$$3(x + 6)(x - 5)$$

D
$$(x - 6)(x + 5)$$

Solution

Given: $$3x^{2} - 3x - 90$$
$$= 3(x^{2} - x - 30)$$ {Taking $$3$$ as common}
$$=3 (x^{2} - 6x + 5x - 30)$$
$$= 3 (x (x -6) + 5 (x - 6))$$
$$= 3(x - 6)(x + 5)$$
Question 5
1 / -0

Factorise: $$\displaystyle 5xy+15y$$

A
$$\displaystyle 5y(x+1)$$

B
$$\displaystyle 5y(x+3)$$

C
$$\displaystyle 5y(x+y)$$

D
$$\displaystyle 5y(x+5)$$

Solution

$$\displaystyle 5xy+15y=\left( 5\times x\times y \right) +\left( 5\times 3\times y \right) $$

$$\displaystyle =5y\left( x+3 \right) $$
Question 6
1 / -0

Factorisation of the expression $$\displaystyle { x }^{ 4 }yz+x{ y }^{ 4 }z+xy{ z }^{ 4 }$$ results in:

A
$$\displaystyle xyz\left( { x }^{ 2 }+{ y }^{ 2 }+{ z }^{ 2 } \right) $$

B
$$\displaystyle xyz\left( { x }^{ 3 }+{ y }^{ 3 }+{ z }^{ 3 } \right) $$

C
$$\displaystyle { x }^{ 3 }{ y }^{ 3 }{ z }^{ 3 }\left( x+y+z \right) $$

D
$$\displaystyle { x }^{ 2 }{ y }^{ 2 }{ z }^{ 2 }\left( { x }^{ 2 }+{ y }^{ 2 }+{ z }^{ 2 } \right) $$

Solution

$$\displaystyle { x }^{ 4 }yz+x{ y }^{ 4 }z+xy{ z }^{ 4 }$$

$$=\displaystyle xyz( { x }^{ 3 }+{ y }^{ 3 }+{ z }^{ 3 } ) $$
Question 7
1 / -0

Factorisation of the expression : $$\displaystyle -2{ x }^{ 2 }{ y }^{ 3 }+6{ x }^{ 3 }{ y }^{ 2 }-8{ x }^{ 2 }{ y }^{ 2 }$$ results in :

A
$$\displaystyle -2{ x }^{ 2 }{ y }^{ 2 }\left( -y-3x-4 \right) $$

B
$$-\displaystyle 2{ x }^{ 2 }{ y }^{ 2 }\left( y-3x+4 \right) $$

C
$$\displaystyle 2{ x }^{ 2 }{ y }^{ 2 }\left( 3x+y-4 \right) $$

D
$$\displaystyle 2{ x }^{ 2 }{ y }^{ 2 }\left( 3x-y+4 \right) $$

Solution

$$\displaystyle -2{ x }^{ 2 }{ y }^{ 3 }+6{ x }^{ 3 }{ y }^{ 2 }-8{ x }^{ 2 }{ y }^{ 2 }$$

$$\displaystyle =\left[ (-2)\times { x }^{ 2 }\times { y }^{ 2 }\times y \right] +\left[ (-2) \times (-3)\times { x }^{ 2 }\times x\times { y }^{ 2 } \right] +\left[(-2) \times 4 \times { x }^{ 2 }\times { y }^{ 2 }\right]$$

$$\displaystyle =-2{ x }^{ 2 }{ y }^{ 2 }\left( y-3x+4 \right) $$

$$\displaystyle =-2{ x }^{ 2 }{ y }^{ 2 }\left( y-3x-4 \right) $$
Question 8
1 / -0

Factorise: $$\displaystyle -6{ a }^{ 2 }+6cb-6ca$$

A
$$\displaystyle -6\left( { a }^{ 2 }+cb-ca \right) $$

B
$$\displaystyle 6\left( { a }^{ 2 }-cb+ca \right) $$

C
$$\displaystyle 6\left( { a }^{ 2 }+cb+ca \right) $$

D
$$\displaystyle -6\left( { a }^{ 2 }-cb+ca \right) $$

Solution

$$ -6{ a }^{ 2 }+6cb-6ca=\left( -6\times a\times a \right) +\left( 6\times c\times b \right) -\left( 6\times c\times a \right) $$

$$\displaystyle =-6( { a }^{ 2 }-cb+ca) $$
Question 9
1 / -0

Factorise : $$\displaystyle 12{ x }^{ 2 }-24{ y }^{ 2 }+36{ z }^{ 2 }$$

A
$$\displaystyle 12{ x }^{ 2 }-2{ y }^{ 2 }+3{ z }^{ 2 }$$

B
$$\displaystyle 12\left( { x }^{ 2 }-2{ y }^{ 2 }+3{ z }^{ 2 } \right) $$

C
$$\displaystyle 12\left( { x }^{ 2 }-{ y }^{ 2 }+{ z }^{ 2 } \right) $$

D
$$\displaystyle 12\left( { x }^{ 2 }+{ y }^{ 2 }+{ z }^{ 2 } \right) $$

Solution

$$\displaystyle 12{ x }^{ 2 }-24{ y }^{ 2 }+36{ z }^{ 2 }=12x^2 - 12\times 2y^2 + 12\times 3z^2$$

$$=12\left( { x }^{ 2 }-2{ y }^{ 2 }+3{ z }^{ 2 } \right) $$
Question 10
1 / -0

Factorisation of the expression : $$\displaystyle 7{ a }^{ 2 }-49{ b }^{ 2 }$$

A
$$\displaystyle 7\left( { a }^{ 2 }-7{ b }^{ 2 } \right) $$

B
$$\displaystyle 7{ a }^{ 2 }-7{ b }^{ 2 }$$

C
$$\displaystyle 7\left( { a }^{ 2 }-{ b }^{ 2 } \right) $$

D
$$\displaystyle 7\left( 7{ a }^{ 2 }-{ b }^{ 2 } \right) $$

Solution

$$\displaystyle 7{ a }^{ 2 }-49{ b }^{ 2 }=( 7\times a\times a) -( 7\times 7\times b\times b ) $$

$$\displaystyle = 7( { a }^{ 2 }-7{ b }^{ 2 } ) $$

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Re-Attempt Weekly Quiz Competition

Factorisation Test - 21

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Factorisation Test - 21

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Question 1

$$\displaystyle 4x-7$$

$$\displaystyle 3$$

$$\displaystyle 6$$

$$\displaystyle 7$$

Solution

Question 2

$$\displaystyle xy(x-y)$$

$$\displaystyle 65xy(x-y)$$

$$\displaystyle 13xy(x-5y)$$

$$\displaystyle 13xy(x-y)$$

Solution

Question 3

$$\displaystyle 5x( 3-{ x }^{ 2 }) $$

$$\displaystyle 5x( { x }^{ 2 }-3) $$

$$\displaystyle -5x( { x }^{ 2 }-3 ) $$

$$\displaystyle x( { x }^{ 2 }-3) $$

Solution

Question 4

$$(x + 6)(x - 5)$$

$$3(x - 6)(x + 5)$$

$$3(x + 6)(x - 5)$$

$$(x - 6)(x + 5)$$

Solution

Question 5

$$\displaystyle 5y(x+1)$$

$$\displaystyle 5y(x+3)$$

$$\displaystyle 5y(x+y)$$

$$\displaystyle 5y(x+5)$$

Solution

Question 6

$$\displaystyle xyz\left( { x }^{ 2 }+{ y }^{ 2 }+{ z }^{ 2 } \right) $$

$$\displaystyle xyz\left( { x }^{ 3 }+{ y }^{ 3 }+{ z }^{ 3 } \right) $$

$$\displaystyle { x }^{ 3 }{ y }^{ 3 }{ z }^{ 3 }\left( x+y+z \right) $$

$$\displaystyle { x }^{ 2 }{ y }^{ 2 }{ z }^{ 2 }\left( { x }^{ 2 }+{ y }^{ 2 }+{ z }^{ 2 } \right) $$

Solution

Question 7

$$\displaystyle -2{ x }^{ 2 }{ y }^{ 2 }\left( -y-3x-4 \right) $$

$$-\displaystyle 2{ x }^{ 2 }{ y }^{ 2 }\left( y-3x+4 \right) $$

$$\displaystyle 2{ x }^{ 2 }{ y }^{ 2 }\left( 3x+y-4 \right) $$

$$\displaystyle 2{ x }^{ 2 }{ y }^{ 2 }\left( 3x-y+4 \right) $$

Solution

Question 8

$$\displaystyle -6\left( { a }^{ 2 }+cb-ca \right) $$

$$\displaystyle 6\left( { a }^{ 2 }-cb+ca \right) $$

$$\displaystyle 6\left( { a }^{ 2 }+cb+ca \right) $$

$$\displaystyle -6\left( { a }^{ 2 }-cb+ca \right) $$

Solution

Question 9

$$\displaystyle 12{ x }^{ 2 }-2{ y }^{ 2 }+3{ z }^{ 2 }$$

$$\displaystyle 12\left( { x }^{ 2 }-2{ y }^{ 2 }+3{ z }^{ 2 } \right) $$

$$\displaystyle 12\left( { x }^{ 2 }-{ y }^{ 2 }+{ z }^{ 2 } \right) $$

$$\displaystyle 12\left( { x }^{ 2 }+{ y }^{ 2 }+{ z }^{ 2 } \right) $$

Solution

Question 10

$$\displaystyle 7\left( { a }^{ 2 }-7{ b }^{ 2 } \right) $$

$$\displaystyle 7{ a }^{ 2 }-7{ b }^{ 2 }$$

$$\displaystyle 7\left( { a }^{ 2 }-{ b }^{ 2 } \right) $$

$$\displaystyle 7\left( 7{ a }^{ 2 }-{ b }^{ 2 } \right) $$

Solution

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