# Free Factorisation 03 Practice Test - 8th Grade

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

A.

3

B.

m+2

C.

m+3

D.

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.

One of the factors of x22x15 is:

A.

x+3

B.

x-3

C.

x+5

D.

x - 15

#### SOLUTION

Solution : A

The given expression is

x22x15

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

=x25x+3x15=x(x5)+3(x5)
=(x+3)(x5)

So, x+3 is one of the factors of the given expression.

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

A.

p = 7, q = 2

B.

p = 2, q = 7

C.

p = 14, q = 3

D.

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.

Which of the following is the expression obtained by the division of 5pq(p2q2) by 2p(p+q)?

A.

5q(pq)4

B.

5q(p+q)2

C.

5q(pq)2

D.

5q(p+q)4

#### SOLUTION

Solution : C

Given, the expression is
5pq(p2q2).

[Using the identity: a2b2=(a+b)(ab)]

5pq(p2q2)=5pq(p+q)(pq)

Now dividing the above expression by
2p(p+q),we get

5pq(p+q)(pq)2p(p+q)

=5q(pq)2

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

A.

True

B.

False

#### SOLUTION

Solution : A

The given expression is
(2x)2+5x

Substituting 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

State whether true or false:
(3x2+1)(3x2)=1+1=2

A.

True

B.

False

#### SOLUTION

Solution : B

3x2+13x2

=3x23x2+13x2

=1+13x2

Hence, the given statement is false.

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

A.

True

B.

False

#### SOLUTION

Solution : A

5(x+2y)=5x+5×2y=5x+10y

Division of 72x2y4z6 by 8x2y2z3 gives 9y2z3

A.

True

B.

False

#### SOLUTION

Solution : A

728=9y4y2=y2z6z3=z3

Therefore, 72x2y4z68x2y2z3=9y2z3

Substituting x=3 in (x2)5x gives

___

#### SOLUTION

Solution :

Substituting x=3 in x25x gives
(3)25(3)=9+15=24

Which of the following is a factor of x26x16?

A.

x+8

B.

x8

C.

x2

D.

x6

#### SOLUTION

Solution : B

The given algebraic equation is x26x16.
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, 82=6.
So, we split the expression as shown
x2+2x8x16
=x(x+2)8(x+2)
=(x+2)(x8)
Hence x8 is a factor of the given expression.