Factorisation Test

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Factorisation Test - 16

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Question 1
1 / -0

Factorize : $$4ax + 4ay$$

A
$$4a(x + y)$$

B
$$4(x + y)$$

C
$$4a(x - y)$$

D
$$4(x - y)$$

Solution

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

Factorize the below equation:
$$b(a+d) -c(a+d)$$

A
$$(a - c)(b + d)$$

B
$$(b + c)(a - d)$$

C
$$(b - c)(a + d)$$

D
None of these

Solution

The common factor between $$b(a+d)$$ and $$c(a+d)$$ is $$(a+d)$$ that is the HCF of $$b(a+d)$$ and $$c(a+d)$$ is $$(a+d)$$.
Therefore, we take $$(a+d)$$ as a common factor in the expression $$b(a+d)-c(a+d)$$ as shown below:
$$b(a+d)-c(a+d)=(a+d)(b-c)$$
Hence, the factorization of $$b(a+d)-c(a+d)$$ is $$(b-c)(a+d)$$.
Question 3
1 / -0

$$\displaystyle \left( { 3x }^{ 2 }-x \right) \div \left( -x \right) $$ is equal to

A
$$\displaystyle 3x+1$$

B
$$\displaystyle -3x-1$$

C
$$\displaystyle -3x+1$$

D
$$\displaystyle 3x-1$$

Solution

$$\displaystyle \left( { 3x }^{ 2 }-x \right) \div \left( -x \right)$$
By separating denominators, we get
$$ =\dfrac { 3{ x }^{ 2 } }{ -x } +\dfrac { \left( -x \right) }{ \left( -x \right) } =-3x+1$$
Hence, final result after given operation is $$-3x+1$$.
Question 4
1 / -0

One of the factor of $$(25x^2-1)+(1+5x^2)$$ is

A
$$5+x$$

B
$$5-x$$

C
$$5x-1$$

D
$$10x$$

Solution

Given, $$(25x^2-1)+(1+5x^2)=30x^2=(3x)(10x)$$
Clearly, $$10x$$ is factor of $$(25x^2-1)+(1+5x^2)$$
Option D is correct.
Question 5
1 / -0

Factorise $$ax^2y + bxy^2 + cxyz$$

A
$$x(ax+by+cz)$$

B
$$y(ax-by-cz)$$

C
$$xy(ax+by+cz)$$

D
$$xy(a+by+cz)$$

Solution

We have, $$ax^2y =a \times x \times x \times y$$
$$ bxy^2 = b \times x \times y \times y$$
and, $$cxyz= c \times x \times y \times z$$
The three terms have x and y as common factors
$$\therefore ax^2y + bxy^2 + cxyz = (a \times x \times x \times y) + (b \times x \times y \times y) +(c \times x \times y \times z) $$
$$= x \times y \times (a \times x +b \times y + c \times z) $$
$$=xy(ax+by+ cz)$$
Question 6
1 / -0

Which of the following is factorization of $$(-56mnp^2 + 7mnp).$$

A
$$7mnp(-8p + 1)$$

B
$$7mnp(8p + 1)$$

C
$$7mnp(8p - 1)$$

D
None of these

Solution

$$-56mnp^2+7mnp$$
$$=-7\times 8mnp^2+7mnp$$
$$=7mnp(-8p+1)$$
Question 7
1 / -0

Factorise :
$$\displaystyle 121ac-16a^{2}b^{2}$$

A
$$a(121c-16ab^{2})$$

B
$$a(121c+16ab^{2})$$

C
$$a(121c-16ac^{2})$$

D
none of these

Solution

$$121ac-16a^2b^2$$
$$=121\times a\times c-16\times a\times a\times b\times b$$
$$=a(121c-16ab^2)$$
Question 8
1 / -0

Which of the following is an example of factorisation?

A
$$x^2+2x=x(x+2)$$

B
$$x^2+2x=x(x+1)$$

C
$$x^2+2x=x(x+3)$$

D
None of the above

Solution

The common factor between $$x^2$$ and $$2x$$ is $$x$$ that is the HCF of $$x^2$$ and $$2x$$ is $$x$$.

Therefore, we take $$x$$ as a common factor in the expression $$x^2+2x$$ as shown below:

$$x^2+2x=x(x+2)$$

Hence, the factorization of $$x^2+2x$$ is $$x(x+2)$$.
Question 9
1 / -0

Factorise $$\displaystyle 4m^{3}n^{2}+12m^{2}n^{2}+18m^{4}n^{3}$$

A
$$\displaystyle m^{3}n^{3}(m+3mn+4m^{2}n)$$

B
$$\displaystyle m^{2}n^{2}(5m+2n+6m^{2}n)$$

C
$$\displaystyle 2m^{2}n^{2}(2m+6+9m^{2}n)$$

D
None of these

Solution

The factorization of $$\displaystyle 4m^{3}n^{2}+12m^{2}n^{2}+18m^{4}n^{3}$$ is
$$2m^{2}n^{2}(2m+6+9m^{2}n)$$ ....Taking $$2m^2n^2$$ common
Question 10
1 / -0

Factorise $$10a^2 -15b^2 + 20c^2$$

A
$$5(a^2 -3b^2 + 4c^2)$$

B
$$10(2a^2 +3b^2 - 4c^2)$$

C
$$5(2a^2 -3b^2 + 4c^2)$$

D
$$10(a^2 -b^2 + 4c^2)$$

Solution

We have, $$10a^2= 2 \times 5 \times a \times a,$$
$$15b^2 = 3 \times 5 \times b \times b$$
and,$$ 20c^2= 2 \times 2 \times 5 \times c \times c $$
The three terms have 5 as a common factor
$$10a^2 - 15b^2+ 20c^2 = (2 \times 5 \times a \times a)-(3 \times 5 \times b \times b) +(2 \times 2 \times 5\times c \times c)$$
=$$5 \times (2 \times a \times a-3 \times b\times b + 4 \times c \times c) $$
=$$ 5(2a^2 -3b^2 + 4c^2)$$

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Factorisation Test - 16

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Factorisation Test - 16

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Question 1

$$4a(x + y)$$

$$4(x + y)$$

$$4a(x - y)$$

$$4(x - y)$$

Solution

Question 2

$$(a - c)(b + d)$$

$$(b + c)(a - d)$$

$$(b - c)(a + d)$$

None of these

Solution

Question 3

$$\displaystyle 3x+1$$

$$\displaystyle -3x-1$$

$$\displaystyle -3x+1$$

$$\displaystyle 3x-1$$

Solution

Question 4

$$5+x$$

$$5-x$$

$$5x-1$$

$$10x$$

Solution

Question 5

$$x(ax+by+cz)$$

$$y(ax-by-cz)$$

$$xy(ax+by+cz)$$

$$xy(a+by+cz)$$

Solution

Question 6

$$7mnp(-8p + 1)$$

$$7mnp(8p + 1)$$

$$7mnp(8p - 1)$$

None of these

Solution

Question 7

$$a(121c-16ab^{2})$$

$$a(121c+16ab^{2})$$

$$a(121c-16ac^{2})$$

none of these

Solution

Question 8

$$x^2+2x=x(x+2)$$

$$x^2+2x=x(x+1)$$

$$x^2+2x=x(x+3)$$

None of the above

Solution

Question 9

$$\displaystyle m^{3}n^{3}(m+3mn+4m^{2}n)$$

$$\displaystyle m^{2}n^{2}(5m+2n+6m^{2}n)$$

$$\displaystyle 2m^{2}n^{2}(2m+6+9m^{2}n)$$

None of these

Solution

Question 10

$$5(a^2 -3b^2 + 4c^2)$$

$$10(2a^2 +3b^2 - 4c^2)$$

$$5(2a^2 -3b^2 + 4c^2)$$

$$10(a^2 -b^2 + 4c^2)$$

Solution

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