Factorisation Test

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Factorisation Test - 18

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Question 1
1 / -0

Factorise: $$9x^3-6x^2+ 12x$$

A
$$3x (3x^2-2x + 4)$$

B
$$x (3x^2-2x + 4)$$

C
$$x (3x^2-2x - 4)$$

D
$$3x (3x^2-x + 7)$$

Solution

factorising $$9x^3-6x^2+ 12x$$
Take $$3x$$ as common,
$$=3x (3x^2-2x + 4)$$
Question 2
1 / -0

Factorise:
$$12x + 15$$

A
$$3(4x + 5)$$

B
$$(4x + 5)$$

C
$$3(4x - 5)$$

D
None of the Above

Solution

$$12x + 15$$
Taking 3 as common,
$$3(4x + 5)$$
Answer $$3(4x + 5)$$
Question 3
1 / -0

Factorise:
$$6a(a -2b) + 5b(a -2b)$$

A
$$(a-b) (6a + 5b)$$

B
$$(a-2b) (6a + 5b)$$

C
$$(a-2b) (3a + 5b)$$

D
$$(a-b) (3a + 5b)$$

Solution

$$6a(a -2b) + 5b(a -2b)$$
taking (a -2b) common,
$$=(a-2b) (6a + 5b)$$
Question 4
1 / -0

Evaluate: $$\displaystyle \left( 21x-35 \right) \div 7$$

A
$$\displaystyle 2x-5$$

B
$$\displaystyle 4x-5$$

C
$$\displaystyle 3x-5$$

D
$$\displaystyle 5x-3$$

Solution

$$\displaystyle \left( 21x-35 \right) \div 7=\frac { 21x-35 }{ 7 } $$

$$=\dfrac { 7\left( 3x-5 \right) }{ 7 } =3x-5$$
Question 5
1 / -0

Simplify: $$\displaystyle 9\left( { a }^{ 4 }{ b }^{ 6 }-{ a }^{ 6 }{ b }^{ 4 } \right) \div 3{ a }^{ 4 }{ b }^{ 4 }$$

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

B
$$\displaystyle 3(a-b)$$

C
$$\displaystyle 3\left( { a }^{ 2 }-{ b }^{ 2 } \right) $$

D
$$\displaystyle 3\left( { b }^{ 2 }-{ a }^{ 2 } \right) $$

Solution

$$\displaystyle 9\left( { a }^{ 4 }{ b }^{ 6 }-{ a }^{ 6 }{ b }^{ 4 } \right) \div 3{ a }^{ 4 }{ b }^{ 4 }=\frac { 9\left( { a }^{ 4 }{ b }^{ 6 }-{ a }^{ 6 }{ b }^{ 4 } \right) }{ 3{ a }^{ 4 }{ b }^{ 4 } } $$

$$\displaystyle =\frac { 9{ a }^{ 4 }{ b }^{ 4 }\left( { b }^{ 2 }-{ a }^{ 2 } \right) }{ 3{ a }^{ 4 }{ b }^{ 4 } } $$

$$\displaystyle = 3\left( { b }^{ 2 }-{ a }^{ 2 } \right) $$
Question 6
1 / -0

Divide: $$\displaystyle \left( { x }^{ 8 }{ y }^{ 7 }{ z }^{ 6 }-{ z }^{ 6 }{ y }^{ 7 }{ x }^{ 8 } \right) $$ by $$\displaystyle { y }^{ 7 }{ x }^{ 8 }{ z }^{ 6 }$$

A
$$\displaystyle -1$$

B
$$\displaystyle 1$$

C
$$\displaystyle 0$$

D
$$\dfrac 12$$

Solution

$$\displaystyle \left( { x }^{ 8 }{ y }^{ 7 }{ z }^{ 6 }-{ z }^{ 6 }{ y }^{ 7 }{ x }^{ 8 } \right) \div { y }^{ 7 }{ x }^{ 8 }{ z }^{ 6 }$$

$$\displaystyle =\frac { { x }^{ 8 }{ y }^{ 7 }{ z }^{ 6 }-{ x }^{ 8 }{ y }^{ 7 }{ z }^{ 6 } }{ { x }^{ 8 }{ y }^{ 7 }{ z }^{ 6 } } =\frac { 0 }{ { x }^{ 8 }{ y }^{ 7 }{ z }^{ 6 } } =0$$
Question 7
1 / -0

Evaluate: $$\displaystyle \left( 4{ x }^{ 8 }-{ 5x }^{ 6 }+{ 6x }^{ 4 } \right) \div { x }^{ 4 }$$

A
$$\displaystyle { 4x }^{ 4 }-{ 5x }^{ 10 }+6x$$

B
$$\displaystyle { 4x }^{ 5 }-{ 5x }^{ 3 }+6x$$

C
$$\displaystyle { 4x }^{ 3 }-5x+6$$

D
$$\displaystyle { 4x }^{ 4 }-{ 5x }^{ 2 }+6$$

Solution

$$\displaystyle \left( 4{ x }^{ 8 }-{ 5x }^{ 6 }+{ 6x }^{ 4 } \right) \div { x }^{ 4 }=\frac { 4{ x }^{ 8 }-{ 5x }^{ 6 }+{ 6x }^{ 4 } }{ { x }^{ 4 } } $$

$$\displaystyle =\frac { { x }^{ 4 }\left( { 4x }^{ 4 }-{ 5x }^{ 2 }+6 \right) }{ { x }^{ 4 } } $$

$$\displaystyle ={ 4x }^{ 4 }-{ 5x }^{ 2 }+6$$
Question 8
1 / -0

Divide: $$\displaystyle \left( -16{ x }^{ 6 }-24{ x }^{ 4 } \right) $$ by $$\displaystyle \left( -{ 8x }^{ 3 } \right) $$

A
$$\displaystyle { 2x }^{ 3 }+3x$$

B
$$\displaystyle { 2x }^{ 2 }+3$$

C
$$\displaystyle -{ 2x }^{ 3 }-3x$$

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

Solution

$$\displaystyle \left( -16{ x }^{ 6 }-24{ x }^{ 4 } \right) \div \left( -{ 8x }^{ 3 } \right) =\frac { -16{ x }^{ 6 }-24{ x }^{ 4 } }{ -{ 8x }^{ 3 } } $$

$$\displaystyle =\frac { -8{ x }^{ 4 }\left( { 2x }^{ 2 }+3 \right) }{ { 8x }^{ 3 } } $$

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

$$\displaystyle = { 2x }^{ 3 }+3x$$
Question 9
1 / -0

Evaluate : $$\displaystyle 21{ x }^{ 3 }{ y }^{ 3 }+35{ x }^{ 4 }{ y }^{ 2 }-56{ x }^{ 2 }{ y }^{ 4 }\div -7{ x }^{ 2 }{ y }^{ 2 }$$

A
$$\displaystyle -5{ x }^{ 2 }+3xy+8{ y }^{ 2 }$$

B
$$\displaystyle 8{ y }^{ 2 }-3xy-5{ x }^{ 2 }$$

C
$$\displaystyle 5{ x }^{ 2 }+3xy-8{ y }^{ 2 }$$

D
$$\displaystyle 5{ x }^{ 2 }-3xy+8{ y }^{ 2 }$$

Solution

$$\displaystyle 21{ x }^{ 3 }{ y }^{ 3 }+35{ x }^{ 4 }{ y }^{ 2 }-56{ x }^{ 2 }{ y }^{ 4 }\div -7{ x }^{ 2 }{ y }^{ 2 }$$

$$\displaystyle = \frac { 21{ x }^{ 3 }{ y }^{ 3 }+35{ x }^{ 4 }{ y }^{ 2 }-56{ x }^{ 2 }{ y }^{ 4 } }{ -7{ x }^{ 2 }{ y }^{ 2 } } $$

$$\displaystyle = \frac { 7{ x }^{ 2 }{ y }^{ 2 }\left( 3xy+5{ x }^{ 2 }-8{ y }^{ 2 } \right) }{ -7{ x }^{ 2 }{ y }^{ 2 } } $$

$$\displaystyle =-\left( 3xy+5{ x }^{ 2 }-8{ y }^{ 2 } \right) $$

$$\displaystyle = 8{ y }^{ 2 }-3xy-5{ x }^{ 2 }$$
Question 10
1 / -0

Divide: $$\displaystyle 8\left( { x }^{ 3 }{ y }^{ 2 }{ z }^{ 2 }+{ x }^{ 2 }{ y }^{ 3 }{ z }^{ 2 }+{ x }^{ 2 }{ y }^{ 2 }{ z }^{ 3 } \right) \div 2{ x }^{ 2 }{ y }^{ 2 }{ z }^{ 2 }$$

A
$$\displaystyle 4(y+z)$$

B
$$\displaystyle 4(x)$$

C
$$\displaystyle 4(x+y+z)$$

D
$$\displaystyle 4x+4y+z$$

Solution

$$\displaystyle 8\left( { x }^{ 3 }{ y }^{ 2 }{ z }^{ 2 }+{ x }^{ 2 }{ y }^{ 3 }{ z }^{ 2 }+{ x }^{ 2 }{ y }^{ 2 }{ z }^{ 3 } \right) \div 2{ x }^{ 2 }{ y }^{ 2 }{ z }^{ 2 }$$

$$\displaystyle =\frac { 8\left( { x }^{ 3 }{ y }^{ 2 }{ z }^{ 2 }+{ x }^{ 2 }{ y }^{ 3 }{ z }^{ 2 }+{ x }^{ 2 }{ y }^{ 2 }{ z }^{ 3 } \right) }{ 2{ x }^{ 2 }{ y }^{ 2 }{ z }^{ 2 } } $$

$$\displaystyle =\frac { 8{ x }^{ 2 }{ y }^{ 2 }{ z }^{ 2 }\left( x+y+z \right) }{ 2{ x }^{ 2 }{ y }^{ 2 }{ z }^{ 2 } } $$

$$\displaystyle =4\left( x+y+z \right) $$

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Re-Attempt Weekly Quiz Competition

Factorisation Test - 18

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Factorisation Test - 18

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Question 1

$$3x (3x^2-2x + 4)$$

$$x (3x^2-2x + 4)$$

$$x (3x^2-2x - 4)$$

$$3x (3x^2-x + 7)$$

Solution

Question 2

$$3(4x + 5)$$

$$(4x + 5)$$

$$3(4x - 5)$$

None of the Above

Solution

Question 3

$$(a-b) (6a + 5b)$$

$$(a-2b) (6a + 5b)$$

$$(a-2b) (3a + 5b)$$

$$(a-b) (3a + 5b)$$

Solution

Question 4

$$\displaystyle 2x-5$$

$$\displaystyle 4x-5$$

$$\displaystyle 3x-5$$

$$\displaystyle 5x-3$$

Solution

Question 5

$$\displaystyle 3(b-a)$$

$$\displaystyle 3(a-b)$$

$$\displaystyle 3\left( { a }^{ 2 }-{ b }^{ 2 } \right) $$

$$\displaystyle 3\left( { b }^{ 2 }-{ a }^{ 2 } \right) $$

Solution

Question 6

$$\displaystyle -1$$

$$\displaystyle 1$$

$$\displaystyle 0$$

$$\dfrac 12$$

Solution

Question 7

$$\displaystyle { 4x }^{ 4 }-{ 5x }^{ 10 }+6x$$

$$\displaystyle { 4x }^{ 5 }-{ 5x }^{ 3 }+6x$$

$$\displaystyle { 4x }^{ 3 }-5x+6$$

$$\displaystyle { 4x }^{ 4 }-{ 5x }^{ 2 }+6$$

Solution

Question 8

$$\displaystyle { 2x }^{ 3 }+3x$$

$$\displaystyle { 2x }^{ 2 }+3$$

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

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

Solution

Question 9

$$\displaystyle -5{ x }^{ 2 }+3xy+8{ y }^{ 2 }$$

$$\displaystyle 8{ y }^{ 2 }-3xy-5{ x }^{ 2 }$$

$$\displaystyle 5{ x }^{ 2 }+3xy-8{ y }^{ 2 }$$

$$\displaystyle 5{ x }^{ 2 }-3xy+8{ y }^{ 2 }$$

Solution

Question 10

$$\displaystyle 4(y+z)$$

$$\displaystyle 4(x)$$

$$\displaystyle 4(x+y+z)$$

$$\displaystyle 4x+4y+z$$

Solution

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