Factorisation Test

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Factorisation Test - 11

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Weekly Quiz Competition

Question 1
1 / -0

Factorise $$a^3 - a^2 + a$$

A
$$a(a^2 - a - 1)$$

B
$$a(a^2 + a + 1)$$

C
$$(a^2 - a + 1)$$

D
$$a(a^2 - a + 1)$$
Question 2
1 / -0

Factorise: $$5t+25t^2$$

A
$$5t(1+5t)$$

B
$$t(1-5t)$$

C
$$5t(1-5t)$$

D
$$t(1+5t)$$

Solution

$$5t+25t^2$$
$$=5t(1+5t)$$
Question 3
1 / -0

Divide the given polynomial by the given monomial.
$$(x^3 + 2x^2 + 3x)\div 2x$$

A
$$\dfrac{1}{2}(x^2+2x+3)$$

B
$$\dfrac{1}{4}(x^2-2x+3)$$

C
$$\dfrac{1}{2}(x^2-2x+3)$$

D
$$\dfrac{1}{2}(x^2+2x-3)$$

Solution

$$(x^{ 3 }+2x^{ 2 }+3x)\div 2x$$
$$=\dfrac{(x^{ 3 }+2x^{ 2 }+3x)}{2x}$$
$$=\dfrac{x(x^2+2x+3)}{2x}$$
$$=\dfrac{(x^2+2x+3)}{2}$$
Question 4
1 / -0

Divide the given polynomial by the given monomial.
$$8(x^3y^2z^2 + x^2y^3z^2 + x^2y^2z^3)\div 4x^2y^2z^2$$

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

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

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

D
$$4(x + y + z)$$

Solution

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

$$=\dfrac{8(x^{ 3 }y^{ 2 }z^{ 2 }+x^{ 2 }y^{ 3 }z^{ 2 }+x^{ 2 }y^{ 2 }z^{ 3 })}{4x^{ 2 }y^{ 2 }z^{ 2 }}$$

$$=\dfrac{8x^2y^2z^2(x+y+z)}{4x^{ 2 }y^{ 2 }z^{ 2 }}$$

$$=2(x+y+z)$$
Question 5
1 / -0

Factorize $$3a^{2}-9ab$$ by taking common factors.

A
$$3a\left ( a-3b \right )$$

B
$$3a\left ( a-b \right )$$

C
$$3a\left ( 3a-b \right )$$

D
$$3a\left ( a+b \right )$$

Solution

$$3a^{2}-9ab$$
$$3$$ and $$a$$ are common in the above two terms in the addition, so taking these as common.
$$3a^2-9ab=3a(a-3b)$$
Option A is correct.
Question 6
1 / -0

Factorise: $$4x-8y$$

A
$$4(x-4y)$$

B
$$3(x-y)$$

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

D
$$4(x-2y)$$

Solution

$$4x-8y$$
$$=4(x-2y)$$
Question 7
1 / -0

Factorise $$15 x + 5$$

A
$$5(3x + 1)$$

B
$$5(x+1)$$

C
$$3(5x+1)$$

D

$$15(x+1)$$

Solution

$$ 15x+5$$
$$= (5\times 3 \times x) + (5\times1)$$
$$= 5(3\times x +1) $$
$$= 5(3x+1)$$
Question 8
1 / -0

Factorise $$9b-12x$$

A
$$2(3b + 4x)$$

B
$$3(b - 4x)$$

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

D
$$2(3b - x)$$

Solution

$$Factorizing\quad 9b-12x,\\ 3*\frac { 9b-12x }{ 3 } \quad =3(3b-4x)$$
Question 9
1 / -0

Factorise $$4a^2 - 8 ab$$

A
$$4a(a + 2b)$$

B
$$4a(a - b)$$

C
$$4a(a - 2b)$$

D
$$a(a - 2b)$$

Solution

Given expression is $$4a^2-8ab$$.

Taking $$4a$$ common from both terms of $$4a^2-8ab$$, we get:
$$4a(a-2b)$$

Hence, $$4a^2-8ab=4a(a-2b)$$.
Question 10
1 / -0

Factorise: $$3x^2 + 6x^3$$

A
$$3x^2 (1 + 2x)$$

B
$$3x^2 (1 - 2x)$$

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

D
$$3x^2 (1 + x)$$

Solution

$$Factorizing:\quad { 3x }^{ 2 }+{ 6x }^{ 3 },\\ we\quad take\quad 3{ x }^{ 2 }\quad common,\\ =3{ x }^{ 2 }(1+2x)$$

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Re-Attempt Weekly Quiz Competition

Factorisation Test - 11

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Factorisation Test - 11

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SHARING IS CARING

Question 1

$$a(a^2 - a - 1)$$

$$a(a^2 + a + 1)$$

$$(a^2 - a + 1)$$

$$a(a^2 - a + 1)$$

Question 2

$$5t(1+5t)$$

$$t(1-5t)$$

$$5t(1-5t)$$

$$t(1+5t)$$

Solution

Question 3

$$\dfrac{1}{2}(x^2+2x+3)$$

$$\dfrac{1}{4}(x^2-2x+3)$$

$$\dfrac{1}{2}(x^2-2x+3)$$

$$\dfrac{1}{2}(x^2+2x-3)$$

Solution

Question 4

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

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

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

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

Solution

Question 5

$$3a\left ( a-3b \right )$$

$$3a\left ( a-b \right )$$

$$3a\left ( 3a-b \right )$$

$$3a\left ( a+b \right )$$

Solution

Question 6

$$4(x-4y)$$

$$3(x-y)$$

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

$$4(x-2y)$$

Solution

Question 7

$$5(3x + 1)$$

$$5(x+1)$$

$$3(5x+1)$$

$$15(x+1)$$

Solution

Question 8

$$2(3b + 4x)$$

$$3(b - 4x)$$

$$3(3b - 4x)$$

$$2(3b - x)$$

Solution

Question 9

$$4a(a + 2b)$$

$$4a(a - b)$$

$$4a(a - 2b)$$

$$a(a - 2b)$$

Solution

Question 10

$$3x^2 (1 + 2x)$$

$$3x^2 (1 - 2x)$$

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

$$3x^2 (1 + x)$$

Solution

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