Factorisation Test

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Factorisation Test - 19

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Weekly Quiz Competition

Question 1
1 / -0

Find the value of $$\displaystyle \left( { 3x }^{ 3 }+{ 2x }^{ 2 }+x \right) \div 4x$$

A
$$\displaystyle { 3x }^{ 2 }+2x+1$$

B
$$\displaystyle \frac { 1 }{ 4 } \left( { 3x }^{ 2 }+2x+1 \right) $$

C
$$\displaystyle { 3x }^{ 2 }+2x+\frac { 1 }{ 4 } $$

D
$$\displaystyle 3x+2$$

Solution

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

$$\displaystyle =\frac { x\left( { 3x }^{ 2 }+2x+1 \right) }{ 4x } $$

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

Find the value of $$\displaystyle \left( { 7a }^{ 6 }-8{ a }^{ 5 }+9{ a }^{ 4 } \right) \div { a }^{ 3 }$$

A
$$\displaystyle { 7a }^{ 3 }-{ 8a }^{ 2 }+9a$$

B
$$\displaystyle { 7a }^{ 2 }-8a+9$$

C
$$\displaystyle { 7a }^{ 4 }-{ 8a }^{ 2 }+9a$$

D
$$\displaystyle { 7a }^{ 2 }-{ 8a }^{ 2 }+9a$$

Solution

$$\displaystyle \left( { 7a }^{ 6 }-8{ a }^{ 5 }+9{ a }^{ 4 } \right) \div { a }^{ 3 }=\frac { { 7a }^{ 6 }-8{ a }^{ 5 }+9{ a }^{ 4 } }{ { a }^{ 3 } } $$

$$\displaystyle =\frac { { a }^{ 3 }\left( { 7a }^{ 3 }-{ 8a }^{ 2 }+9a \right) }{ { a }^{ 3 } } $$

$$\displaystyle = { 7a }^{ 3 }-{ 8a }^{ 2 }+9a$$
Question 3
1 / -0

Solve: $$\displaystyle 3{ x }^{ 3 }-15{ x }^{ 2 }+21x\div 3x$$

A
$$\displaystyle x+5+7x$$

B
$$\displaystyle { x }^{ 2 }+5x+7$$

C
$$\displaystyle 3{ x }^{ 2 }-5x+7$$

D
$$\displaystyle { x }^{ 2 }-5x+7$$

Solution

$$\displaystyle 3{ x }^{ 3 }-15{ x }^{ 2 }+21x\div 3x$$

$$\displaystyle = \frac { 3{ x }^{ 3 } }{ 3x } -\frac { 15{ x }^{ 2 } }{ 3x } +\frac { 21x }{ 3x } $$

$$\displaystyle ={ x }^{ 2 }-5x+7$$
Question 4
1 / -0

Simplify: $$\displaystyle \left( 16{ x }^{ 3 }{ y }^{ 2 }{ z }^{ 2 }+16{ x }^{ 2 }{ y }^{ 2 }{ z }^{ 3 }+16{ x }^{ 2 }{ y }^{ 3 }{ z }^{ 2 } \right) \div 8xyz$$

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

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

C
$$\displaystyle 2{ x }^{ 2 }yz+2xy{ z }^{ 2 }+2x{ y }^{ 2 }z$$

D
$$\displaystyle 2{ x }^{ 2 }{ y }^{ 2 }z+2x{ y }^{ 2 }{ z }^{ 2 }+2{ x }^{ 2 }y{ z }^{ 2 }-xyz$$

Solution

Given, $$\displaystyle \left( 16{ x }^{ 3 }{ y }^{ 2 }{ z }^{ 2 }+16{ x }^{ 2 }{ y }^{ 2 }{ z }^{ 3 }+16{ x }^{ 2 }{ y }^{ 3 }{ z }^{ 2 } \right) \div 8xyz$$

$$\displaystyle =\frac { 16{ x }^{ 3 }{ y }^{ 2 }{ z }^{ 2 }+16{ x }^{ 2 }{ y }^{ 2 }{ z }^{ 3 }+16{ x }^{ 2 }{ y }^{ 3 }{ z }^{ 2 } }{ 8xyz } $$

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

$$\displaystyle =2{ x }^{ 2 }yz+2xy{ z }^{ 2 }+2x{ y }^{ 2 }z$$
Question 5
1 / -0

Divide $$\displaystyle (2x+12)$$ by $$\displaystyle (4x+24)$$

A
$$\displaystyle 2$$

B
$$\dfrac 12$$

C
$$\dfrac 14$$

D
$$\dfrac {1}{x+6}$$

Solution

$$\displaystyle \left( 2x+12 \right) \div \left( 4x+24 \right) =\frac { 2x+12 }{ 4x+24 } $$

$$=\dfrac { 2\left( x+6 \right) }{ 4\left( x+6 \right) } =\dfrac { 1 }{ 2 } $$
Question 6
1 / -0

Simplify: $$\displaystyle \left( { a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 }-{ a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 }+{ a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 } \right) \div { a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 }$$

A
$$\displaystyle 1$$

B
$$\displaystyle -1$$

C
$$\displaystyle 0$$

D
None of these

Solution

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

$$\displaystyle =\frac { { a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 }-{ a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 }+{ a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 } }{ { a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 } } $$

$$= \dfrac {0 + a^2b^2c^3}{a^2b^2c^3}$$

$$\displaystyle =\frac { { a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 } }{ { a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 } } =1$$
Question 7
1 / -0

Which of the following statement is correct?

A
$$\displaystyle \left( { x }^{ 2 }-2xy \right) \div x=\left( x-2 y \right) $$

B
$$\displaystyle \left( { x }^{ 2 }-2xy \right) \div x=\left( x-2 \right) $$

C
$$\displaystyle \left( { x }^{ 2 }-2xy \right) \div x=\left( 2x-2y \right) $$

D
$$\displaystyle \left( { x }^{ 2 }-2xy \right) \div x=\left( x-y \right) $$

Solution

$$\displaystyle \left( { x }^{ 2 }-2xy \right) \div x$$

$$=\dfrac { { x }^{ 2 }-2xy }{ x } =\dfrac { x\left( x-2y \right) }{ x } $$

$$=\left( x-2y \right) $$

$$\displaystyle \therefore \left( { x }^{ 2 }-2xy \right) \div x=\left( x-2y \right) $$ is a correct statement.
Question 8
1 / -0

Simplify: $$\displaystyle \frac { 36ab\left( a+2 \right) \left( a+3 \right) }{ 12a\left( a+3 \right) } $$

A
$$\displaystyle 3a(a+2)$$

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

C
$$\displaystyle 3b(a+2)$$

D
$$\displaystyle 3ab+2$$

Solution

$$\displaystyle \frac { 36ab\left( a+2 \right) \left( a+3 \right) }{ 12a\left( a+3 \right) } =\frac { 3b\left( a+2 \right) }{ 1 } =3b\left( a+2 \right) $$
Question 9
1 / -0

The value of $$(\displaystyle 9{ x }^{ 2 }+18x+27) \div 9$$ is equal to

A
$$\displaystyle x+2$$

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

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

D
$$\displaystyle { x }^{ 2 }+2x+1$$

Solution

$$(\displaystyle 9{ x }^{ 2 }+18x+27) \div 9 =\frac { 9{ x }^{ 2 }+18x+27 }{ 9 } $$

$$\displaystyle =\frac { 9\left( { x }^{ 2 }+2x+3 \right) }{ 9 } $$

$$\displaystyle = { x }^{ 2 }+2x+3$$
Question 10
1 / -0

Divide $$\displaystyle ( 36{ x }^{ 2 }-4 )$$ by $$\left( 6x-2 \right) $$

A
$$\displaystyle 3x-1$$

B
$$\displaystyle 3x+1$$

C
$$\displaystyle 6x-2$$

D
$$\displaystyle 6x+2$$

Solution

$$\displaystyle \left( 36{ x }^{ 2 }-4 \right) \div \left( 6x-2 \right) =\frac { 36{ x }^{ 2 }-4 }{ 6x-2 } $$

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

$$\displaystyle =6x+2$$

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Re-Attempt Weekly Quiz Competition

Factorisation Test - 19

Result

Factorisation Test - 19

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SHARING IS CARING

Question 1

$$\displaystyle { 3x }^{ 2 }+2x+1$$

$$\displaystyle \frac { 1 }{ 4 } \left( { 3x }^{ 2 }+2x+1 \right) $$

$$\displaystyle { 3x }^{ 2 }+2x+\frac { 1 }{ 4 } $$

$$\displaystyle 3x+2$$

Solution

Question 2

$$\displaystyle { 7a }^{ 3 }-{ 8a }^{ 2 }+9a$$

$$\displaystyle { 7a }^{ 2 }-8a+9$$

$$\displaystyle { 7a }^{ 4 }-{ 8a }^{ 2 }+9a$$

$$\displaystyle { 7a }^{ 2 }-{ 8a }^{ 2 }+9a$$

Solution

Question 3

$$\displaystyle x+5+7x$$

$$\displaystyle { x }^{ 2 }+5x+7$$

$$\displaystyle 3{ x }^{ 2 }-5x+7$$

$$\displaystyle { x }^{ 2 }-5x+7$$

Solution

Question 4

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

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

$$\displaystyle 2{ x }^{ 2 }yz+2xy{ z }^{ 2 }+2x{ y }^{ 2 }z$$

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

Solution

Question 5

$$\displaystyle 2$$

$$\dfrac 12$$

$$\dfrac 14$$

$$\dfrac {1}{x+6}$$

Solution

Question 6

$$\displaystyle 1$$

$$\displaystyle -1$$

$$\displaystyle 0$$

None of these

Solution

Question 7

$$\displaystyle \left( { x }^{ 2 }-2xy \right) \div x=\left( x-2 y \right) $$

$$\displaystyle \left( { x }^{ 2 }-2xy \right) \div x=\left( x-2 \right) $$

$$\displaystyle \left( { x }^{ 2 }-2xy \right) \div x=\left( 2x-2y \right) $$

$$\displaystyle \left( { x }^{ 2 }-2xy \right) \div x=\left( x-y \right) $$

Solution

Question 8

$$\displaystyle 3a(a+2)$$

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

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

$$\displaystyle 3ab+2$$

Solution

Question 9

$$\displaystyle x+2$$

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

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

$$\displaystyle { x }^{ 2 }+2x+1$$

Solution

Question 10

$$\displaystyle 3x-1$$

$$\displaystyle 3x+1$$

$$\displaystyle 6x-2$$

$$\displaystyle 6x+2$$

Solution

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