Factorisation Test

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Factorisation Test - 17

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Question 1
1 / -0

Factorise : $$5mn+15mnp$$

A
$$5mn(1 + 3p)$$

B
$$3mn(1 + 5p)$$

C
$$5mn(1 - 3p)$$

D
none of these

Solution

The common factor between $$5mn$$ and $$15mnp$$ is $$5mn$$ that is the HCF of $$5mn$$ and $$15mnp$$ is $$5mn$$.

Therefore, we take $$5mn$$ as a common factor in the expression $$5mn+15mnp$$ as shown below:

$$5mn+15mnp=5mn(1+3p)$$

Hence, the factorization of $$5mn+15mnp$$ is $$5mn(1+3p)$$.
Question 2
1 / -0

$$\displaystyle (6ab-3abc+9abcd)\div \left( -\frac { 1 }{ 3 } ab \right) $$ is equal to

A
$$\displaystyle 2+c+3cd$$

B
$$\displaystyle -2+c-3cd$$

C
$$\displaystyle -18+9c-27cd$$

D
$$\displaystyle 18-9c-27cd$$

Solution

$$\displaystyle \frac { 6ab-3abc+9abcd }{ -\frac { 1 }{ 3 } ab } $$

By separating denominators, we get

$$\displaystyle =\dfrac { 6ab }{ -\frac { 1 }{ 3 } ab } +\frac { \left( -3abc \right) }{ -\frac { 1 }{ 3 } ab } +\frac { 9abcd }{ -\frac { 1 }{ 3 } ab } $$

$$\displaystyle =\frac { 6ab }{ ab } \times (-3)+\frac { \left( -3abc \right) }{ ab } \times (-3)+\frac { \left( 9abcd \right) }{ ab } \times (-3)$$

$$\displaystyle =-18+9c-27cd$$
Hence final value after given operation is $$-18+9c-27cd$$
Question 3
1 / -0

Factorise : $$6xy^2 + 4x^2y$$

A
$$2xy(3x+y)$$

B
$$xy(3x+2y)$$

C
$$2xy(2x+3y)$$

D
none of these

Solution

The common factor between $$6xy^2$$ and $$4x^2y$$ is $$2xy$$ that is the HCF of $$6xy^2$$ and $$4x^2y$$ is $$2xy$$.
Therefore, we take $$2xy$$ as a common factor in the expression $$6xy^2+4x^2y$$ as shown below:
$$6xy^2+4x^2y=2xy(2x+3y)$$
Hence, the factors of $$6xy^2+4x^2y$$ are $$2xy$$ and $$(2x+3y)$$.
Question 4
1 / -0

Evaluate $$8 (x^3 y^2 z^2 + x^2y^3z^2 + x^2y^2z^3) \div 4x^2y^2z^2$$

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

B
$$2(x-y+z)$$

C
$$2(x+y-z)$$

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

Solution

$$8(x^3 y^2 z^2 + x^2 y^3 z^2 + x^2 y^2 z^3) \div 4x^2 y^2 z^2$$
$$= \displaystyle \frac{8 (x^3 y^2 z^2 + z^2 y^3 z^2 + x^2 y^2 z^3)}{4 x^2 y^2 z^2}$$
$$\displaystyle = \frac{8 \times x^2 y^2 z^2 (x + y + z)}{4 x^2 y^2 z^2} = 2 (x + y + z)$$
Question 5
1 / -0

Divide:
$$8x^2y^2-6xy^2 +10x^2y^3$$ by $$2xy$$

A
$$4y -3y + 5xy^3$$

B
$$4xy -3y - 5xy^3$$

C
$$4x -3y - 5xy^2$$

D
$$4xy -3y + 5xy^2$$

Solution

$$8x^2y^2-6xy^2 +10x^2y^3 \div 2xy$$
$$\displaystyle \frac { 8x^{ 2 }y^{ 2 }-6xy^{ 2 }+10x^{ 2 }y^{ 3 } }{ 2xy } $$
$$=\displaystyle \frac { 2xy(4xy-6y+10xy^{ 2 }) }{ 2xy } $$
$$=4xy-3y+5xy^{ 2 }$$
Question 6
1 / -0

Simplify: $$\displaystyle \left( { 8m }^{ 2 }-9m \right) \div 3m$$

A
$$\displaystyle \frac { 1 }{ 3 } \left( 8m-9 \right) $$

B
$$\displaystyle 8m-9$$

C
$$\displaystyle \frac { 1 }{ 3 } \left( 8m-3 \right) $$

D
$$\displaystyle 5m-3$$

Solution

$$\displaystyle \left( { 8m }^{ 2 }-9m \right) \div 3m=\frac { { 8m }^{ 2 }-9m }{ 3m } $$

$$\displaystyle =\frac { m\left( 8m-9 \right) }{ 3m } $$

$$\displaystyle =\frac { 8m-9 }{ 3 } $$

$$\displaystyle = \frac { 1 }{ 3 } \left( 8m-9 \right) $$
Question 7
1 / -0

Evaluate: $$\displaystyle \left( { 7a }^{ 2 }-5a \right) \div 5a$$

A
$$\displaystyle 7a-1$$

B
$$\displaystyle 7a-5$$

C
$$\displaystyle \frac { 1 }{ 5 } \left( 7a-5 \right) $$

D
$$\displaystyle \frac { 1 }{ 5 } \left( 7a-1 \right) $$

Solution

$$\displaystyle \left( { 7a }^{ 2 }-5a \right) \div 5a=\frac { { 7a }^{ 2 }-5a }{ 5a }$$

=$$\dfrac { a\left( 7a-5 \right) }{ 5a } =\dfrac { 1 }{ 5 } \left( 7a-5 \right) $$
Question 8
1 / -0

Evaluate: $$\displaystyle ( 6{ x }^{ 2 }-4x) \div 2x$$

A
$$\displaystyle 2x-3$$

B
$$\displaystyle 3x-2$$

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

D
$$\displaystyle 12x-8$$

Solution

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

$$=\dfrac { 2x\left( 3x-2 \right) }{ 2x } $$

$$\displaystyle =3x-2$$
Question 9
1 / -0

Simplify: $$\displaystyle \left( 12a-36 \right) \div 6$$

A
$$\displaystyle 2a+6$$

B
$$\displaystyle a-3$$

C
$$\displaystyle 2a-6$$

D
$$\displaystyle a+3$$

Solution

$$\displaystyle \left( 12a-36 \right) \div 6=\frac { 12a-36 }{ 6 } =\frac { 12\left( a-3 \right) }{ 6 } $$

$$\displaystyle =2\left( a-3 \right) $$

$$\displaystyle =2a-6$$
Question 10
1 / -0

Evaluate $$(p^3 q^6 -p^6 q^3) \div p^3 q^3$$

A
$$q^3+p^3$$

B
$$q^3-p^3$$

C
$$q^2-p^2$$

D
$$q^2+p^2$$

Solution

$$\begin{aligned}{}\left( {{p^3}{q^6} - {p^6}{q^3}} \right) \div {p^3}{q^3} &= \frac{{{p^3}{q^6} - {p^6}{q^3}}}{{{p^3}{q^3}}}\\ &= \frac{{{p^3}{q^3}\left( {{q^3} - {p^3}} \right)}}{{{p^3}{q^3}}}\\& = {q^3} - {p^3}\end{aligned}$$

Hence, option $$B$$ is correct.

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Factorisation Test - 17

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Factorisation Test - 17

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SHARING IS CARING

Question 1

$$5mn(1 + 3p)$$

$$3mn(1 + 5p)$$

$$5mn(1 - 3p)$$

none of these

Solution

Question 2

$$\displaystyle 2+c+3cd$$

$$\displaystyle -2+c-3cd$$

$$\displaystyle -18+9c-27cd$$

$$\displaystyle 18-9c-27cd$$

Solution

Question 3

$$2xy(3x+y)$$

$$xy(3x+2y)$$

$$2xy(2x+3y)$$

none of these

Solution

Question 4

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

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

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

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

Solution

Question 5

$$4y -3y + 5xy^3$$

$$4xy -3y - 5xy^3$$

$$4x -3y - 5xy^2$$

$$4xy -3y + 5xy^2$$

Solution

Question 6

$$\displaystyle \frac { 1 }{ 3 } \left( 8m-9 \right) $$

$$\displaystyle 8m-9$$

$$\displaystyle \frac { 1 }{ 3 } \left( 8m-3 \right) $$

$$\displaystyle 5m-3$$

Solution

Question 7

$$\displaystyle 7a-1$$

$$\displaystyle 7a-5$$

$$\displaystyle \frac { 1 }{ 5 } \left( 7a-5 \right) $$

$$\displaystyle \frac { 1 }{ 5 } \left( 7a-1 \right) $$

Solution

Question 8

$$\displaystyle 2x-3$$

$$\displaystyle 3x-2$$

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

$$\displaystyle 12x-8$$

Solution

Question 9

$$\displaystyle 2a+6$$

$$\displaystyle a-3$$

$$\displaystyle 2a-6$$

$$\displaystyle a+3$$

Solution

Question 10

$$q^3+p^3$$

$$q^3-p^3$$

$$q^2-p^2$$

$$q^2+p^2$$

Solution

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