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Published on: 07/09/2019
Factorisation
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Questions + Answers key
Take MCQ Mathematics Test
1.
Factorise (m8-n8) and after this divide by (m4+n4)
2.
Using the suitable identities, evaluate the following :
(103) 2 .
3.
Factorise the expressions and divide them as directed.4yz(z2+ 6z - 16) \(\div \) 2y(z + 8)
4.
Factotise the following expressions. q2 - 10q +21
5.
Foetorise the following expressions. a4 - 2a2b2 + b4
6.
Divide 21(y + 3) (y2 -16) by 7(y2 - y -12).
7.
Find the common factors of the given terms 14pq = 28 p2q2
8.
Factorise each of the following algebraic expressions. axy + bcxy - az - bcz
9.
Find the greatest common factor of the given monomials.27a2b3c2,9ab2,c2, 18a2 bc2
10.
Find and correct the errors in the following mathematical statements. (3x+ 2)2 = 3x2 + 6x+ 4
11.
Factorise 37x(x - 1)(x +2)
12.
Factorise 81x(x + 4)
13.
a (b + c) = ab + ac is
commutative property
distributive property
associative property
closure property
14.
An irreducible factor of 24x2 y2 is
x2
y2
x
24x
15.
Which of the following is a binomial?
7 x a +a
6a2 + 7b + 2c
4a + 3b x 2c
6(a2 +b)
16.
In a polynomial, the exponents of the variables are always
integers
positive integers
non-negative integers
non-positive integers
17.
The greatest common factor of 6a and 12b is
6
2
3
1
18.
The irreducible factorisation of 3a3 + 6a is 3(a2 + 2).
19.
The value of p for 512 - 492 = 100p is 2.
20.
Some of the factors of \(\frac { { n }^{ 2 } }{ 2 } +\frac { n }{ 2 } are\frac { 1 }{ 2 } \) , n (n+1)
21.
The sum of areas of two squares with sides 5a and 5b is 25(a +b)(a -b).
22.
An identity is true for all values of its variables.
23.
The factorisation of 3x + 15z is
24.
1052 -1032 =....... x (105 -103) =..............
25.
Volume of a rectangular box with length 2x, breadth 3y and height 4z is..........
26.
On simplification, \(\frac { 7y+7 }{ 7 } \)
27.
Number of factors of (a + b)2 is.......
1.
(m+n)(m-n)(m2+n2)
2.
10609
3.
∵ z2+ 6z - 16 = z2+ 8z - 2z - 16
∵ 8 - 2 = 6
= z(z + 8) - 2(z + 8)8 x 2 = 16
= (z + 8)(z - 2)
\(\therefore \frac { 4yx({ z }^{ 2 }+6z-16) }{ 2y(z+8) } \)
\(=\frac { 2\times 2\times y\times z\times (z+8)\times (z-2) }{ 2\times y\times (z+8) } \)
\(=\frac { 2\times z\times (z-2) }{ 1 } =2z(z-2)\)
thus, 4yz(z2 + 6z-16)\(\div \)2y(z + 8) = 2z(z - 2)
4.
Here, ab = 21 and a + b = -10
Possible values of a and b are 7, 3 or -7, -3.
But 7 +3 = 10 \(\neq \) - 10 [not possible]
\(\therefore\) a= -7, b = -3
Now q2 - 10q + 21 = q2 +(-7-3)q + 21
= q2 - 7q - 3q + 21
=q (q -7)-3(9 - 7) = (q-7)(q -3)
Hence, required factors of given expression are(q - 7) and (q -3).
5.
a4- 2a2b2 +b4 =(a2)2 - 2(a2)(b)2 + (b2)2
On comparing with a2 - 2ab + b2, we get a = a2 and b = b2
\(\therefore\) (a2)2 -2(a2)(b2) + (b2)2 = (a2 -b2)2
[\(\because\) (a-b)2 =a2 -2ab +b2]
=[(a + b)(a- b)]2
= (a + b)2 (a - b)2
= (a + b)(a + b)(a - b)(a - b)
6.
We have, 21(y + 3)(y2 -16)+ 7(y2 - Y -12)
Factorising 21 (y + 3)(y2 -16)
= 21 (y + 3) {(y)2 - 4 x 4]
= 21 (y + 3) {(y)2 - (4)2}
= 21 (y + 3)(y + 4)(y - 4)
=3 x 7 (y+ 3)(y+ 4)(y-4)
Now, factorising 7(y2 - y -12)
Since,4x(-3)=-12,
4 + (-3) = 1 or 4 - 3 = 1
Putting these values in given expression, we get
7(y2 - y -12)=7 {y2 -(4 - 3)y -12}
=7(y2 -4y+ 3y-12)
=7{(y(y-4)+ 3(y-4)]
= 7 {(y - 4) (y + 3)}= 7(y - 4)(y + 3)
Now, \(\frac { 21(y+3){ y }^{ 2 }-16) }{ 7({ y }^{ 2 }-y-12) } \)
= \(\frac { 3\times 7(y+3)(y+4)(y-4) }{ 7(y-4)(y+3) } \) = 3(y+4)
7.
We have, 14pq = 2 x 7 x p x q
and 28p2q2 = 2 x 2 x 7 x p x p x p x q
The two terms have 2,7, P and q as common factors .
So, common factor of given terms
= 2 x 7 x p x q = 14 pq
8.
(a +bc)(xy - z)
9.
9abc2
10.
Given mathematical statement is incorrect.
Hence, correct statement is
(3x + 2)2 = (3x)2 + 2(3x)(2) + (2)2 = 9x2 + 12x + 4
because the correct formula for (a + b)2 is
(a + b)2 = a2 + 2ab + b2 and here a = 3x, b = 2.
11.
37 x x x (x - 1) x (x + 2)
12.
3 X 3 X 3 X 3 X x X (x + 4)
13.
(b)
distributive property
14.
(c)
x
15.
(d)
6(a2 +b)
16.
(c)
non-negative integers
17.
(a)
6
18.
(b)
19.
(a)
20.
(a)
21.
(b)
22.
(a)
23.
3x + 15z = 3x + 3 x 5z = 3 (x + 5z)
By using distrubutibe property ab +ac = a (b+c)]
24.
1052 - 1032 = (105 +103)(105-103)
=208 x 2 = 416
25.
We know what
Volume of a rectangular box or volume of a cuboid
= length x breadth x Height
= 2x x 3y x 4z = 24xyz
26.
\(\frac { 7y+7 }{ 7 } =\frac { 7(y+1) }{ 7 } =(y+1)\)
27.
(a+b)2 = (a+b)(a+b)
Since this expression contains two factors, hence the required answer is 2
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