# Free Factorisation 03 Practice Test - 8th Grade

### Question 1

Which of the following is/are the irreducible factor(s) of 3m2+9m+6?

3

m+2

m+3

m+1

#### SOLUTION

Solution :A, B, and D

Given, the expression is

3m2+9m+6.

Taking 3 common from the above expression, we get

3(m2+3m+2) ...(i)

Now comparing m2+3m+2 with the identity x2+(a+b)x+ab.

We note that,

(a+b)=3 and ab=2.

So,

2+1=3 and (2)(1)=2

Hence,

m2+3m+2

=m2+2m+m+2

=m(m+2)+1(m+2)

=(m+2)(m+1)

Now from (i), we get

⇒3m2+9m+6=3(m2+3m+2)=3(m+2)(m+1)

Therefore,

3, (m+2) and (m+1) are the 3 irreducible factors of the given expression.

### Question 2

One of the factors of x2−2x−15 is:

x+3

x-3

x+5

x - 15

#### SOLUTION

Solution :A

The given expression is

x2−2x−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

=x2−5x+3x−15=x(x−5)+3(x−5)

=(x+3)(x−5)So, x+3 is one of the factors of the given expression.

### Question 3

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

#### SOLUTION

Solution :A

Since 14 is HCF of 4p and 21q, then both of them should have 7 and 2 as prime factors.

4p = 2 x 2 x p

21q = 3 x 7 x q

Since 14 is the HCF, p should be 7 and q should be 2.

### Question 4

Which of the following is the expression obtained by the division of 5pq(p2−q2) by 2p(p+q)?

5q(p−q)4

5q(p+q)2

5q(p−q)2

5q(p+q)4

#### SOLUTION

Solution :C

Given, the expression is

5pq(p2−q2).

[Using the identity: a2−b2=(a+b)(a−b)]

⇒5pq(p2−q2)=5pq(p+q)(p−q)

Now dividing the above expression by

2p(p+q),we get

5pq(p+q)(p−q)2p(p+q)

=5q(p−q)2

### Question 5

The value of the expression (2x)2+5x for x=3 is 51.

True

False

#### SOLUTION

Solution :A

The given expression is

(2x)2+5xSubstituting x = 3 in the above expression we get

(2×3)2+5×3

62+5×3

36 +15 = 51

Hence, the given statemnet is true

### Question 6

State whether true or false:

(3x2+1)(3x2)=1+1=2

True

False

#### SOLUTION

Solution :B

3x2+13x2

=3x23x2+13x2

=1+13x2

Hence, the given statement is false.

### Question 7

5x+10y is the expanded form of 5(x+2y).

True

False

#### SOLUTION

Solution :A

5(x+2y)=5x+5×2y=5x+10y

### Question 8

Division of 72x2y4z6 by 8x2y2z3 gives 9y2z3

True

False

#### SOLUTION

Solution :A

728=9y4y2=y2z6z3=z3

Therefore, 72x2y4z68x2y2z3=9y2z3

### Question 9

Substituting x=−3 in (x2)−5x gives

#### SOLUTION

Solution :Substituting x=−3 in x2−5x gives

(−3)2−5(−3)=9+15=24

### Question 10

Which of the following is a factor of x2−6x−16?

x+8

x−8

x−2

x−6

#### SOLUTION

Solution :B

The given algebraic equation is x2−6x−16.

We can factorize this using the following identity using,

(x+a)(x+b)=x2+(a+b)x+ab

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

8×2=4×4=16

We can see that, 8−2=6.

So, we split the expression as shown

x2+2x−8x−16

=x(x+2)−8(x+2)

=(x+2)(x−8)

Hence x−8 is a factor of the given expression.