Factorisation(8th Grade > Mathematics ) Questions and answers for exam Preparation

8th Grade > Mathematics

FACTORISATION MCQs

Total Questions : 57 | Page 2 of 6 pages

Question 11. One of the factors of

x^{2} - 2 x - 15

is:

x+3
x-3
x+5
x - 15

Discuss Question

Answer: Option A. -> x+3
:
A
The given expression is

x^{2} - 2 x - 15

We have to split the middle term in such a way the sum is -2 and product is -15 , which can be done in following way

= x^{2} - 5 x + 3 x - 15 = x (x - 5) + 3 (x - 5)

= (x + 3) (x - 5)

So,

x + 3

is one of the factors of the given expression.

Question 12. The value of the expression

(2 x)^{2} + 5 x

for

x = 3

is 51.

True
False
5q(p−q)2
5q(p+q)4

Discuss Question

Answer: Option A. -> True
:
A
The given expression is

(2 x)^{2} + 5 x

Substituting

x

= 3 in the above expression we get

(2 \times 3)^{2} + 5 \times 3

6^{2} + 5 \times 3

36 +15 = 51
Hence, the given statemnet is true

Question 13.

5 x + 10 y

is the expanded form of

5 (x + 2 y)

True
False
5q(p−q)2
5q(p+q)4

Discuss Question

Answer: Option A. -> True
:
A

5 (x + 2 y) = 5 x + 5 \times 2 y = 5 x + 10 y

Question 14. If 14 is the HCF of 4p and 21q, then minimum value of p and q are:

p = 7, q = 2
p = 2, q = 7
p = 14, q = 3
None of the above

Discuss Question

Answer: Option A. -> p = 7, q = 2
:
A
Since 14 is HCF of 4p and 21q, thenboth of them should have 7 and 2 as prime factors.
4p = 2 x 2x p
21q = 3 x 7 x q
Since 14 is the HCF, p should be 7 and q should be 2.

Question 15. Which of the following is a factor of

x^{2} - 6 x - 16

x+8
x−8
x−2
x−6

Discuss Question

Answer: Option B. -> x−8
:
B
The given algebraic equation is

x^{2} - 6 x - 16

.
We can factorize this using the following identity using,

(x + a) (x + b) = x^{2} + (a + b) x + a b

So, we have to first find the factors of 16.

8 \times 2 = 4 \times 4 = 16

We can see that,

8 - 2 = 6

.
So, we split the expression as shown

x^{2} + 2 x - 8 x - 16

= x (x + 2) - 8 (x + 2)

= (x + 2) (x - 8)

Hence

x - 8

is a factor of the given expression.

Question 16. State whether true or false:

\frac{(3 x^{2} + 1)}{(3 x^{2})} = 1 + 1 = 2

True
False
5q(p−q)2
5q(p+q)4

Discuss Question

Answer: Option B. -> False
:
B

\frac{3 x^{2} + 1}{3 x^{2}}

= \frac{3 x^{2}}{3 x^{2}} + \frac{1}{3 x^{2}}

= 1 + \frac{1}{3 x^{2}}

Hence, the given statement is false.

Question 17. Dividing

(a + b)^{2} + (a - b)^{2}

(a^{2} + b^{2})

gives
___

Discuss Question

(a + b)^{2} + (a - b)^{2} = (a^{2} + b^{2} + 2 a b) + (a^{2} + b^{2} - 2 a b) = 2 (a^{2} + b^{2})

Dividing by

a^{2} + b^{2}

we get,
=

\frac{2 (a^{2} + b^{2})}{(a^{2} + b^{2})} = 2

Thus,

\frac{((a + b)^{2} + (a - b)^{2})}{(a^{2} + b^{2})} = 2

Question 18.

Factorise: 25 + 70 x + 49 x^{2}

(5x+7)(5x+2)
(7x+5)(5x+3)
(7x+5)(7x+5)
(3x+7)2

Discuss Question

Answer: Option C. -> (7x+5)(7x+5)
:
C

Given, the expression is 25 + 70 x + 49 x^{2} .

The givenexpression can be rewritten as,

49 x^{2} + 70 x + 25

Using the identity: (a + b)^{2} = a^{2} + 2 a b + b^{2}, we get

49 x^{2} + 70 x + 25 = (7 x)^{2} + 2 (5) (7 x) + 5^{2}

= (7 x + 5)^{2}

= (7 x + 5) (7 x + 5)

∴ 25 + 70 x + 49 x^{2} = (7 x + 5) (7 x + 5)

Question 19. Which of the following is the factorised form of

20 l^{2} m + 30 a l m ?

10lm(l+3a)
10lm(2l+3a)
5lm(2l+3a)
10lm(2l−3a)

Discuss Question

Answer: Option B. -> 10lm(2l+3a)
:
B

Given, the expression is 20 l^{2} m + 30 a l m .

The givenexpression can be factorised as follows :-

20 l^{2} m + 30 a l m

= (2 \times 2 \times 5 \times l \times l \times m) + (2 \times 3 \times 5 \times a \times l \times m)

Taking out the common factors from both the terms, we get

= (2 \times 5 \times l \times m) [(2 \times l) + (3 \times a)]

= 10 l m (2 l + 3 a)

Question 20. Dividing

2 x^{2} + 13 x + 15

x + 5

and then substituting

x = 2

in the resulting expression gives
___

Discuss Question

2 x^{2} + 13 x + 15 = 2 x^{2} + 10 x + 3 x + 15 = 2 x (x + 5) + 3 (x + 5) = \frac{(2 x + 3) (x + 5)}{(x + 5)} = 2 x + 3

Substituting

x = 2

in resulting expression gives

2 \times 2 + 3 = 7

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