This page requires a JavaScript-enabled browser
Instructions on how to enable your browser are contained in the help file.
Factorization, Highest Common Factor, Least Common Multiple and Square Root
1.
ac +bc + ad + bd = (a+b)( __________ ).
a) b+d
b) a+c
c) a+d
d) c+d
2.
x
2
- 81 = (x+9) ( _______ ).
a) x/9
b) x-9
c) x+9
3.
x
2
y
2
-y
2
= y
2
(x+1) ( ________ ).
a) x-1
b) x+1
c) x/1
4.
4x
2
-5xy+y
2
= (4x-y) ( ___________ )
a) (x/y)
b) (x-y)
c) (x+y)
5.
x
2
-3x+2 = ( _____________ ) (x-1).
a) x/2
b) x+2
c) x-2
6.
x
3
+ 8 = (x+2) ( ___________ ).
a) x
2
2x+4
b) x
2
-2x+4
c) x
2
-2x-4
7.
1-27a
3
/ b
3
= ( ___________ ) (1+3a/ b +9a
2
/b
2
)
a) (1-3a/b)
b) (1-3a *b)
c) (1-3a+b)
8.
x
3
+ y
3
+1/x
3
-3y = ( _____________ ) (x
2
+y
2
+1/x
2
-xy-y/x-1)
a) (x+y+1-x)
b) (x-y+1/x)
c) (x+y+1/x)
9.
HCF of (x+2y) and (x
2
_ 4y
2
) is ______________.
a) x+2y
b) x-2y
c) x/2y
10.
HCF of x
2
+3x+2 and x
2
+4x+3 is ______________.
a) x-1
b) x/1
c) x+1
11.
HCF of (x
2
-9), (x+3)
2
is ________________.
a) x-3
b) x/3
c) x+3
12.
LCM of (x+y) and x
2
-y
2
is _____________.
a) x
2
-y
2
b) x
2
-y
-2
c) x
-2
-y
2
13.
LCM of x
2
-x-2 and x
2
-3x+2 is _______________.
a) (x-2)(x-1)(x-1)
b) (x-2)(x-1)(x+1)
c) (x+2)(x-1)(x+1)
14.
Simplified form of 1/x-1 + 1/x+1 = ________________.
a) 2x / x
2
-1
b) 2x / x
-2
-1
c) 2x / x
2
1
15.
Simplified form of [(x-y) (x
2
+xy+y
2
)] � (x
3
-y
3
) is ___________.
a) 2
b) 1
c) -1
16.
Square root of x
2
+18x+81 is _________________.
a) x/9
b) x+9
c) x * 9
17.
Square root of 64x
4
y
2
is ____________________.
a) 8x
2
y
b) 8x
3
y
c) 8x
-2
y
18.
Simplified form of (a
2
+5a-14) x 1/a-2 is
a) (a/7)
b) (a-7)
c) (a+7)
19.
If (x-1) is a factor of (x
3
-7x+m) then m = ______________.
a) 6
b) 4
c) 8
20.
LCM = product of ______________ x produced of non-common factors.
a) Two factors
b) Common factors
c) Mix factors
21.
We can find HCF by two methods, by_____________ and division.
a) Mix factors
b) Complete Square
c) Factorization
22.
The square root of an algebraic expression consists of two expressions, which are __________ of each other.
a) Mix factors
b) Complete Square
c) Additive inverse
23.
According to _____________ theorem, if we get R(x)=0 (remainder is zero), on dividing a polynomial P(x) by x-a then x-a is a factor of the polynomial P(x).
a) Factor
b) AD/BC
c) Complete Square
24.
By factorization we can find the square root of such expressions, which can be expressed as a ______________.
a) Complete Square
b) Mix factors
c) AD/BC
25.
If A, B,C and D are algebraic expressions then A/B � C/D =____ where D
¹
0 , B
¹
0 and C
¹
0.
a) AC/BD
b) AD/BC
c) Mix factors
26.
a
4
+ a
4
= a
8
a) False
b) True
27.
(x
4
-y
4
) � (x
2
-y
2
) = x
2
+ y
2
a) False
b) True
28.
a x a x a = 3a
a) False
b) True
29.
x
3
+ y
3
+z
3
- 3xyz = 1/2 (x+y+z) [(x-y)
2
+ (y-2)
2
+ (z-x)
2
]
a) True
b) False
30.
(x+1) is a factor of x
3
-7x-6.
a) True
b) False
31.
2
3
� 2
2
= 2
a) False
b) True
32.
HCF of Z
2
-4 and Z+2 is (z+2).
a) True
b) False
33.
x-y/x+y � (x+y)/x-y = 1
a) True
b) False
34.
xy
2
z
3
/x
3
y
2
z = xyz
a) False
b) True
35.
(a+b+c)
3
= (a+b+c) (a+b+c)
2
a) False
b) True
36.
Factorization of x
3
+64 is (x+4) (x
2
+4x+16)
a) False
b) True
37.
x
4
+x
2
+1 can also be written as (x
2
-x+1) (x
2
+x+1)
a) True
b) False
38.
If D(x) = x-a then P(x) = (x-a) Qx+Rx as a remainder that is called remainder theorem.
a) True
b) False
39.
HCF is affected by multiplying or dividing the polynomials with any number during the process of finding HCF.
a) True
b) False
40.
By highest common factor two or more than two polynomials, we mean, a highest polynomial that divides completely these polynomials.
a) False
b) True
41.
If H+L =A+B then H3+L3 = A
3
+B
3
where �H� & �L� is stands for HCF and LCM respectively and A,B represents two polynomials.
a) True
b) False
42.
LCM of two or more than two polynomials is a highest degree polynomial which divides completely these polynomials.
a) False
b) True
43.
The relation between LCM and HCF which are represented by �L� and �H� respectively is written by AxB = HxL where �A� & �B� are two algebraic expressions.
a) False
b) True
44.
LCM fo 15x
2
, 45xy and 30 zyx is 80x
2
yz.
a) False
b) True
45.
The square root of a
2
+2ab+2ac+2bc+b
2
+c
2
is + - (a+b+c).
a) False
b) True
46.
(x+1) is not a factor of x
3
-7x-6
a) True
b) False
47.
(x+4) (x+2) = x
2
+5x+4
a) False
b) True
48.
1/2 (2a
2
+2b
2
+2b
2
+2c
2
) = a
2
+b
2
+c
2
a) False
b) True
49.
x
4
+3x
3
-12x
2
-20x+48 is exactly divisible by x
3
+5x
2
-2x-24
a) False
b) True
50.
(a-b) (a
2
+ab+b
2
) x a
2
+ b
2
= (a+b)
(a
2
+b
2
) (a-b) (a+b) (a
2
+ab+b
2
)
a) True
b) False
51.
Factors of x
4
+64 are ___________.
a) (x
2
-4x+8)(x
2
+4x+8)
b) (x+8) (x+4)
c) (x-4) (x+4)
d) (x
2
+4x-8) (x
2
+4x+8)
52.
(x
2
-x+1) (x
2
+x+1) = _________.
a) x
4
+x
2
-1
b) x
8
+x
2
+1
c) x
4
-x
2
+1
d) (x
4
+x
2
+1)
53.
To factorize algebraic expressions of the form ax
2
+bx+c, we find two factors p & q such that p+q=b and ___________.
a) pq =ac
b) p+q =ac
c) p-q =ac
d) q=b
e) p=a
54.
Factorization of 4x
2
+8x+3 is ______________.
a) (2x+3) (2x+1)
b) (2x-3) (2x+1)
c) (2x-3) (2x-1)
d) (x+3) (x+1)
55.
If a+b+c =0 then a
3
+b
3
+c
3
=_____________.
a) 2abc
b) 3a
3
b
3
c
3
c) -3abc
d) 3abc
56.
(x+2y+z) (x
2
+4y
2
+z
2
-2xy-2yz-xz) = _____________.
a) x
3M
-8y
3
+z
3
+6xyz
b) x
3
+8y
3
-z
3
-6xyz
c) x
3
+8y
3
+z
3
+6xyz
d) x
3
+8y
3
+z
3
+12xyz
e) x
5
+8y
5
+z
5
+6xyz
57.
For what value of q, x
2
+16x+q is a complete square = _______________.
a) -8
b) 8
c) -64
d) 64
58.
HCF of 16a
2
b
3
and 48a
3
b
4
is _______________.
a) 16a
2
b
3
b) 8ab
c) 48ab
d) 16a
2
b
2
59.
HCF of l
2
-m
2
and l
4
-m
4
is _______________.
a) None of these
b) l-m
c) l+m
d) l2+m
2
60.
LCM of z
2
x
5
and 4x
4
z
5
is _____________.
a) 4x
5
z
5
b) 4xz
c) 4x
4
z
4
d) x
5
z
5
e) x
4
z
4
61.
LCM of (x
3
-8) and (x
2
+2x+4) is ______________.
a) x
2
-2x+4
b) x
3
-8
c) x
3
+8
d) x
2
+2x+4
62.
LCM of (a+4) and a
3
+64 is _____________.
a) a
3
+64
b) a
2
-4a+16
c) a+4
d) a-4
63.
A and B are two polynomials, A = x
2
-1, H=x-1, L=x
2
-1 then B= __________.
a) x-1
b) x+1
c) x
2
-1
d) x
2
+1
64.
Simplified form of a
2
+b
2
-2ab/a
2
-b
2
is
a) a+b/a-b
b) a
2
-b
2
c) a
2
+b
2
d) (a-b)/a+b
65.
Simplified form of (x-y)/x(x+y) � x
2
-y
2
/x
a) x+y
b) (x-y)
2
c) (x+y)
2
d) 1
e) 1/(x+y)
2
66.
Simplified form of (1+x/1-x ) is ______________.
a) 1+x
b) 1-x
c) 1/1+x
d) 1/1-x
67.
Square root of a
2+4ac+4c
2
is _____________.
a) a-2c
b) a
2
+4c
2
c) + - (a+2c)
d) a
2
-4c
2
68.
Square root of y
4
+ 1/ y
4
+2 is _______________.
a) + - (y
2
+1/y)
b) + - (y-1/y)
c) + - (y
2
- 1/y)
d) + - (y + 1/y)
69.
What will be added in 49x
2
+14y to make it a complete square?
a) 7y
2
b) 2y
2
c) y
d) y
2
70.
Ö
9x
2
-12xy+4y
2
= ___________________
a) + - (3x-2y)
b) + - (3x
2
-2y
2
)
c) + - (3x
2
+2y
2
)
d) + - (3x+2y)
71.
For what value of b, x
2
+bx+25 is a perfect square, b= ______________.
a) 10
b) 2
c) 5x
d) 10x
e) 5
72.
Square root of an algebraic expression can be calculated by ________ methods.
a) Division
b) Division and Multiplication
c) Factorization & Division
d) Factorization
73.
The square root of x
2
+8x+16 consists of two expressions, one is (x+4) and other is _____.
a) - (x+4)
b) + - (x-4)
c) (x+4)
d) + - (x+4)
74.
Simplified form of a
3
-b
3
/(a-b)
2
is ______________.
a) a+b/a - b
b) a
2
+ab+b
2
/a-b
c) a
2
+ab+b
2
/a+b
d) a-b/a+b
75.
Simplified form of (1-2ab)/a
2
+b
2
is ___________.
a) (a-b)
2
/a-b
b) (a+b)
2
/a+b
c) (a+b)
2
/ a
2
+b
2
d) (a-b)
2
/a
2
+b
2
76.
x
2
+ 3x + 2
a) (x+2) (x+1)
b) (x+6)
2
c) (x-2) (x+3)
d) (x+2) (x-3)
77.
x
2
+ 12x +36
a) (x+6)
2
b) (x+2) (x
2
-2x+4)
c) (x+2) (x+1)
d) (x-2) (x+3)
78.
x
4
� 9x
2
a) (x+2) (x
2
-2x+4)
b) (x-2) (x+3)
c) (x
2
-3x) (x
2
-3x)
d) (x
2
+3x) (x
2
-3x)
79.
x
3
+ 8
a) (x
2
-3x) (x
2
-3x)
b) (x+6)
2
c) (x+2) (x
2
-2x+4)
d) (x
2
+3x) (x
2
-3x)
80.
x
2
� x � 6
a) (x-2) (x+3)
b) (x+6)
2
c) (x+2) (x-3)
d) (x+2) (x+1)
81.
a
2
+ab, a
2
� b
2
a) a (a+b) (a-b)
b) (x-2) (x+8) (x
2
+2x+4)
c) (x-2) (x-8) (x
2
+2x+4)
d) (x-2) (x
2
+x +6)
82.
(a-b)
3
, (a-b)
2
a) (x-2) (x
2
+x +6)
b) (a-b)
3
c) a (a+b) (a-b)
d) (x-3) (x-2)
83.
x
2
-5x+6, x-2
a) (x-3) (x-2)
b) (a-b)
3
c) a (a+b) (a-b)
d) (x-2) (x-8) (x
2
+2x+4)
84.
(x
3
-8), x
2
-10x+16
a) (x-2) (x-8) (x
2
+2x+4)
b) a (a+b) (a-b)
c) (x-2) (x
2
+x +6)
d) (a-b)
3
85.
x
2
-4, x
2
-5x+6
a) (x-2) (x+8) (x
2
+2x+4)
b) (x-2) (x
2
-x-6)
c) (x-2) (x-8) (x
2
+2x+4)
d) (x-2) (x
2
+x +6)
86.
x
2
y
3
, x
5
y
2
a) a
2
y
2
b) 5x
2
y
2
c) 5x
2
y
4
d) x
2
y
2
87.
(x
2
-49) , x
2
-4x-21
a) (1+x)
b) (x-7)
c) a
2
y
2
d) (a-b)
88.
5x
2
y
2
, 20 x
4
y
2
a) a
2
y
2
b) 5x
2
y
2
c) 5x
2
y
4
d) x
2
y
2
89.
a-b, a
2
-b
2
, (a-b)
3
a) a
2
y
2
b) (1+x)
c) (a-b)
d) (x-7)
90.
1-x
2
, 1+x
3
a) (1-x)
b) (a-b)
c) (x-7)
d) (1+x)
91.
x
2
+ 1/ x
2
+2
a) +-(x+1/x)
b) +- (3x +2)
c) +-(3x-2y)
d) +-(3x+2y)
92.
9x
2
+12x+4
a) +- (3x +2)
b) +-(3x-2y)
c) +-(3x+2y)
d) +- (x+2y)
2
93.
x
2
+4xy+4y
2
a) +- (3x +2)
b) +- (x+2y)
2
c) +-(3x-2y)
d) +-(3x+2y)
94.
x
4
+ 1/ x
4
+2
a) +- (x
2
+1/x
2
)
b) +- (x+2y)
2
c) +-(x+1/x)
d) +- (x+2y)
2
95.
9x
2
+12xy+4y
2
a) +- (x+2y)
2
b) +-(3x-2y)
c) +-(3x+2y)
d) +-(3x +2)
96.
x
2
+ 3x + 2
a) (x+2) (x-3)
b) (x+2) (x+1)
c) (x+6)
2
d) (x-2) (x+3)
97.
x
2
+ 12x +36
a) (x+2) (x+1)
b) (x+2) (x
2
-2x+4)
c) (x+6)
2
d) (x-2) (x+3)
98.
x
4
� 9x
2
a) (x+2) (x
2
-2x+4)
b) (x-2) (x+3)
c) (x
2
-3x) (x
2
-3x)
d) (x
2
+3x) (x
2
-3x)
99.
x
3
+ 8
a) (x+6)
2
b) (x+2) (x
2
-2x+4)
c) (x
2
-3x) (x
2
-3x)
d) (x
2
+3x) (x
2
-3x)
100.
x
2
� x � 6
a) (x+6)
2
b) (x+2) (x-3)
c) (x-2) (x+3)
d) (x+2) (x+1)
101.
a
2
+ab, a
2
� b
2
a) (x-2) (x
2
+x +6)
b) (x-2) (x+8) (x
2
+2x+4)
c) a (a+b) (a-b)
d) (x-2) (x-8) (x
2
+2x+4)
102.
(a-b)
3
, (a-b)
2
a) a (a+b) (a-b)
b) (x-3) (x-2)
c) (a-b)
3
d) (x-2) (x
2
+x +6)
103.
x
2
-5x+6, x-2
a) a (a+b) (a-b)
b) (x-3) (x-2)
c) (a-b)
3
d) (x-2) (x-8) (x
2
+2x+4)
104.
(x
3
-8), x
2
-10x+16
a) (x-2) (x
2
+x +6)
b) (a-b)
3
c) (x-2) (x-8) (x
2
+2x+4)
d) a (a+b) (a-b)
105.
x
2
-4, x
2
-5x+6
a) (x-2) (x-8) (x
2
+2x+4)
b) (x-2) (x+8) (x
2
+2x+4)
c) (x-2) (x
2
-x-6)
d) (x-2) (x
2
+x +6)
106.
x
2
y
3
, x
5
y
2
a) x
2
y
2
b) a
2
y
2
c) 5x
2
y
2
d) 5x
2
y
4
107.
(x
2
-49) , x
2
-4x-21
a) a
2
y
2
b) (1+x)
c) (a-b)
d) (x-7)
108.
5x
2
y
2
, 20 x
4
y
2
a) 5x
2
y
2
b) 5x
2
y
4
c) a
2
y
2
d) x
2
y
2
109.
a-b, a
2
-b
2
, (a-b)
3
a) (1+x)
b) (a-b)
c) (x-7)
d) a
2
y
2
110.
1-x
2
, 1+x
3
a) (x-7)
b) (1+x)
c) (1-x)
d) (a-b)
111.
x
2
+ 1/ x
2
+2
a) +- (3x +2)
b) +-(3x+2y)
c) +-(3x-2y)
d) +-(x+1/x)
112.
9x
2
+12x+4
a) +- (3x +2)
b) +-(3x-2y)
c) +- (x+2y)
2
d) +-(3x+2y)
113.
x
2
+4xy+4y
2
a) +- (x+2y)
2
b) +- (3x +2)
c) +-(3x-2y)
d) +-(3x+2y)
114.
x
4
+ 1/ x
4
+2
a) +- (x+2y)
2
b) +- (x+2y)
2
c) +-(x+1/x)
d) +- (x
2
+1/x
2
)
115.
9x
2
+12xy+4y
2
a) +-(3x-2y)
b) +-(3x+2y)
c) +-(3x +2)
d) +- (x+2y)
2
This is more feedback!
This is the feedback!
