Mathematics - Factorisation
Exam Duration: 45 Mins Total Questions : 20
Factorisation of xy - pq + qy - px is _______.
- (a)
(y - p) (x + q)
- (b)
(y - p) (x - q)
- (c)
(y + p) (x + q)
- (d)
(y + p) (x - q)
If (x2 + 3x + 5) (x2 - 3x + 5) = m2 - n2, then m = _________.
- (a)
x2 - 3x
- (b)
3x
- (c)
x2 + 5
- (d)
Both (A) and (B)
The factors of \(\frac { { x }^{ 2 } }{ 4 } -\frac { { y }^{ 2 } }{ 9 } \) are_____.
- (a)
\(\left( \frac { x }{ 4 } +\frac { y }{ 9 } \right) \left( \frac { x }{ 4 } -\frac { y }{ 9 } \right) \)
- (b)
\(\left( \frac { x }{ 2 } +\frac { y }{ 9 } \right) \left( \frac { x }{ 2 } -\frac { y }{ 9 } \right) \)
- (c)
\(\left( \frac { x }{ 2 } +\frac { y }{ 3 } \right) \left( \frac { x }{ 2 } -\frac { y }{ 3 } \right) \)
- (d)
Both (A) and (B)
The factors of 15x2 - 26x + 8 are_______.
- (a)
(3x - 4) (5x + 2)
- (b)
(3x - 4) (5x - 2)
- (c)
(3x + 4) (5x - 2)
- (d)
(3x + 4) (5x + 2)
The factors of x2 - 16 are_____.
- (a)
(x2 + 2) (x2 - 2)
- (b)
(x + 4)(x - 4)
- (c)
(x + 2) (x - 2)
- (d)
Does not exist
The factors of \(\sqrt { 3 } { x }^{ 2 }+11x+6\sqrt { 3 } \) are________.
- (a)
(x- 3\(\sqrt { 3 } \)) (\(\sqrt { 3 } \)x + 2)
- (b)
(x-3\(\sqrt { 3 } \)) (\(\sqrt { 3 } \)x - 2)
- (c)
(x+3\(\sqrt { 3 } \)) (\(\sqrt { 3 } \)x - 2)
- (d)
(x+3\(\sqrt { 3 } \)) (\(\sqrt { 3 } \)x + 2)
Factors of x4 - (x - Z)4 are _________.
- (a)
(2x + z) (2x3 + z3 - 2x2)
- (b)
z(x + 2z) (x2 +z2 - x2)
- (c)
z(2x - z)(2x2 - 2xz +z2)
- (d)
z(x- 2z)(2z2 - 2xz +x2)
Factorising (x - y)2 + 4xy - z2, we get
- (a)
(x + Y + z)(x + y - z)
- (b)
(x - Y - z)(x + y - z)
- (c)
(x - y + z)(x + y - z)
- (d)
None of these
The factors of x4 + y4 + x2y2 are_____.
- (a)
(x2 + y2)(x2 + y2 - xy)
- (b)
(x2 + y2)(x2 - y2)
- (c)
(x2 + y2 + xy) (X2 + y2 - xy)
- (d)
Factorisation is not possible
For x2 + 2x + 5 to be a factor of .x4 + px2 + q, the values of p and q must be ________.
- (a)
-2,5
- (b)
5, 25
- (c)
10, 20
- (d)
6, 25
One of the factors of 4(x + y)(3a - b) + 6 (x + y)(2b - 3a) is
- (a)
(2b - 3a)
- (b)
(3a - b)
- (c)
(4a - 3b)
- (d)
(- 3a + 4b)
Divide (32x4Y3 - 16x3y4) by (-8x2y)
- (a)
4x3y2 + 2xy3
- (b)
4x3y- 2xy3
- (c)
- 4x2y2 + 2xy3
- (d)
-4xy2 + 2xy3
One of the factors of (p + q)2 - (a - b)2 + P + q - a + b is
- (a)
(p + q + a + b)
- (b)
(p + q - a + b)
- (c)
(p - q + a - b)
- (d)
(p - q + a + b)
Factorise:(2x + 3y)2 - 5(2x + 3y) - 14.
- (a)
4(2x + 3y)(x + Y - 2)
- (b)
4(2x + 3y)(x + Y + 2)
- (c)
(2x - 3y + 7)(2x - 3y + 2)
- (d)
(2x + 3y - 7)(2x + 3y + 2)
Simplify : \(\frac { -14{ x }^{ 12 }y+{ 8x }^{ 5 }z }{ 2{ x }^{ 2 } } \)
- (a)
x3( - 7x7y + 4z)
- (b)
x2(7x7y - 4z)
- (c)
x2(-7x6y + 2z)
- (d)
x3(7x7y + 4z)
Which of the following is the factor of 12(a2+ 7a)2 -8(a2 + 7a)(2a -1)-15 (2a-1)2 ?
(i) (2a2 + 8a + 3) (ii) (6a2 + 52a - 5) (iii) (3a + 5)
- (a)
Only (i)
- (b)
Both (i) and (ii)
- (c)
Only (ii)
- (d)
All (i), (ii) and (iii)
Which of the following statements is Correct?
- (a)
The factors of an expression are always either algebraic variable or algebraic expression.
- (b)
An irreducible factor is a factor that cannot be expressed further as a product of factors.
- (c)
Every binomial expression can be factorised into two monomial expression.
- (d)
The process of writing a given expression as the product of two or more factors is called multiplication of factors.
Fill in the blanks.
(i) \(\frac { { a }^{ 2 }-{ b }^{ 2 } }{ a(a-b) } -\frac { { ab }^{ 2 }+{ a }^{ 2 }b }{ { ab }^{ 2 } } \) is equal to P.
(ii) \(\frac { 64{ y }^{ 4 }+{ 8y }^{ 3 } }{ { 4y }^{ 3 } } \) is equal to Q.
(iii) When we divide (38a3b3c2 - 19a4b2c) by 19a2bc, the result is kab2c - a2b. Then k = R.
- (a)
P Q R \(\frac { (a+b)(b-a) }{ ab } \) 3(8y+ 1) 2 - (b)
P Q R \(\frac { (a+b)(b-a) }{ ab } \) 3(8y+ 1) 1 - (c)
P Q R \(\frac { (a+b)(a-b) }{ ab } \) 2(8y+1) 1 - (d)
P Q R \(\frac { (a+b)(b-a) }{ ab } \) 2(8y + 1 2
Match the expression given in Column-I to one of their factors given in Column-II.
Column-I | Column-II |
---|---|
P. 9x2 + 24x + 16 | (i) (2x - 4) |
Q. 25x2 + 30x + 9 | (ii) (4x + 1) |
R. 40x2 + 14x + 1 | (iii) (5x + 3) |
S. 4x2-16x+16 | (iv) (3x+4) |
- (a)
P \(\rightarrow\)(iv); Q\(\rightarrow\)(iii); R\(\rightarrow\)(ii); S\(\rightarrow\)(i)
- (b)
P\(\rightarrow\)(iii); Q\(\rightarrow\)(i); R\(\rightarrow\)(iv); S\(\rightarrow\)(ii)
- (c)
P\(\rightarrow\)(ii); Q\(\rightarrow\)(i); R\(\rightarrow\)(iv); S\(\rightarrow\)(iii)
- (d)
P\(\rightarrow\)(iv); Q\(\rightarrow\)(iii); R\(\rightarrow\)(i); S\(\rightarrow\)(ii)
Do as directed.
(i) Factorise: \({ x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } } -3\)
(ii) Find the greatest common factors of 14x2y3, 21x3y2 and 35x4y5z.
(iii) Divide z(5z2 -80)by 5z (z +4).
- (a)
(i) (ii) (iii) \(\left( x-\frac { 1 }{ x } \right) \left( x-\frac { 1 }{ x } -2 \right) \) 7xy2 z - 4 - (b)
(i) (ii) (iii) \(\left( x+\frac { 1 }{ x } \right) \left( x+\frac { 1 }{ x } +2 \right) \) 7x2y z - 4 - (c)
(i) (ii) (iii) \(\left( x-\frac { 1 }{ x } +1 \right) \left( x-\frac { 1 }{ x } -1 \right) \) 7x2y2 z - 4 - (d)
(i) (ii) (iii) \(\left( x-\frac { 1 }{ x } -1 \right) \left( x+\frac { 1 }{ x } +1 \right) \) 7x2y2 z - 2