x2 + 2(5x + 12) in the form of factors is :
(x - 6)(x + 4)
(x - 6)(x - 4)
(x + 6)(x + 4)
(x + 6)(x - 4)
Answer
Given,
x2 + 2(5x + 12)
= x2 + 10x + 24
= x2 + 6x + 4x + 24
= x(x + 6) + 4(x + 6)
= (x + 4)(x + 6).
Hence, Option 3 is the correct option.
x(2x - 5) + 3 in the form of factors is :
(x + 1)(2x - 3)
(x + 1)(2x + 3)
(x - 1)(2x + 3)
(x - 1)(2x - 3)
Answer
Given,
x(2x - 5) + 3
= 2x2 - 5x + 3
= 2x2 - 3x - 2x + 3
= x(2x - 3) - 1(2x - 3)
= (x - 1)(2x - 3).
Hence, Option 4 is the correct option.
6x2 - 2 - 4x in the form of factors is :
2(x - 1)(3x - 1)
2(x - 1)(3x + 1)
(2x - 1)(3x - 1)
(6x - 2)(x + 1)
Answer
Given,
6x2 - 2 - 4x
= 6x2 - 4x - 2
= 6x2 - 6x + 2x - 2
= 6x(x - 1) + 2(x - 1)
= (x - 1)(6x + 2)
= 2(x - 1)(3x + 1).
Hence, Option 2 is the correct option.
x(x - 1) - 20 in the form of factors is :
(x - 5)(x + 4)
(x - 5)(x - 4)
(x + 5)(x - 4)
(x + 5)(x + 4)
Answer
Given,
x(x - 1) - 20
= x2 - x - 20
= x2 - 5x + 4x - 20
= x(x - 5) + 4(x - 5)
= (x - 5)(x + 4).
Hence, Option 1 is the correct option.
5 - x(6 - x) in the form of factors is :
(1 - x)(5 + x)
(1 + x)(5 + x)
(1 - x)(5 - x)
(1 + x)(5 - x)
Answer
Given,
5 - x(6 - x)
= 5 - 6x + x2
= x2 - 6x + 5
= x2 - 5x - x + 5
= x(x - 5) - 1(x - 5)
= (x - 1)(x - 5)
= [-(1 - x).-(5 - x)]
= (1 - x)(5 - x).
Hence, Option 3 is the correct option.
Factorise :
1 - 2a - 3a2
Answer
Given,
1 - 2a - 3a2
= -(3a2 + 2a - 1)
= -[3a2 + 3a - a - 1]
= -[3a(a + 1) - 1(a + 1)]
= -(3a - 1)(a + 1)
= (1 - 3a)(a + 1).
Hence, 1 - 2a - 3a2 = (1 - 3a)(a + 1).
Factorise :
24a3 + 37a2 - 5a
Answer
Given,
24a3 + 37a2 - 5a
= 24a3 + 40a2 - 3a2 - 5a
= 8a2(3a + 5) - a(3a + 5)
= (8a2 - a)(3a + 5)
= a(8a - 1)(3a + 5).
Hence, 24a3 + 37a2 - 5a = a(8a - 1)(3a + 5).
Factorise :
3 - a(4 + 7a)
Answer
Given,
3 - a(4 + 7a)
= 3 - 4a - 7a2
= -7a2 - 4a + 3
= -(7a2 + 4a - 3)
= -[7a2 + 7a - 3a - 3]
= -[7a(a + 1) - 3(a + 1)]
= -[(a + 1)(7a - 3)]
= -[-(a + 1)(3 - 7a)]
= (a + 1)(3 - 7a).
Hence, 3 - a(4 + 7a) = (a + 1)(3 - 7a).
Factorise :
(2a + b)2 - 6a - 3b - 4
Answer
Given,
(2a + b)2 - 6a - 3b - 4
= (2a + b)2 - 3(2a + b) - 4
Substituting (2a + b) = x, we get :
= x2 - 3x - 4
= x2 - 4x + x - 4
= x(x - 4) + 1(x - 4)
= (x - 4)(x + 1)
= (2a + b - 4)(2a + b + 1).
Hence, (2a + b)2 - 6a - 3b - 4 = (2a + b - 4)(2a + b + 1).
Factorise :
1 - 2a - 2b - 3(a + b)2
Answer
Given,
1 - 2a - 2b - 3(a + b)2
= 1 - 2(a + b) - 3(a + b)2
Substituting (a + b) = x, we get :
= 1 - 2x - 3x2
= -3x2 - 2x + 1
= -[3x2 + 2x - 1]
= -[3x2 + 3x - x - 1]
= -[3x(x + 1) - 1(x + 1)]
= -[(x + 1)(3x - 1)]
= -[-(x + 1)(1 - 3x)]
= (x + 1)(1 - 3x)
= (a + b + 1)[1 - 3(a + b)]
= (a + b + 1)(1 - 3a - 3b).
Hence, 1 - 2a - 2b - 3(a + b)2 = (a + b + 1)(1 - 3a - 3b).
Factorise :
3a2 - 1 - 2a
Answer
Given,
3a2 - 1 - 2a
= 3a2 - 2a - 1
= 3a2 - 3a + a - 1
= 3a(a - 1) + 1(a - 1)
= (a - 1)(3a + 1).
Hence, 3a2 - 1 - 2a = (a - 1)(3a + 1).
Factorise :
x2 + 3x + 2 + ax + 2a
Answer
Given,
x2 + 3x + 2 + ax + 2a
= x2 + 3x + 2 + a(x + 2)
= x2 + 2x + x + 2 + a(x + 2)
= x(x + 2) + 1(x + 2) + a(x + 2)
= (x + 2)(x + 1 + a).
Hence, x2 + 3x + 2 + ax + 2a = (x + 2)(x + 1 + a).
Factorise :
(3x - 2y)2 + 3(3x - 2y) - 10
Answer
Given,
(3x - 2y)2 + 3(3x - 2y) - 10
Substituting (3x - 2y) = a, we get :
⇒ a2 + 3a - 10
= a2 + 5a - 2a - 10
= a(a + 5) - 2(a + 5)
= (a + 5)(a - 2)
= (3x - 2y + 5)(3x - 2y - 2).
Hence, (3x - 2y)2 + 3(3x - 2y) - 10 = (3x - 2y + 5)(3x - 2y - 2).
Factorise :
5 - (3a2 - 2a)(6 - 3a2 + 2a)
Answer
Given,
5 - (3a2 - 2a)(6 - 3a2 + 2a)
= 5 - [-(3a2 - 2a)(3a2 - 2a - 6)]
= 5 + (3a2 - 2a)(3a2 - 2a - 6)
Substituting 3a2 - 2a = x, we get :
= 5 + x(x - 6)
= 5 + x2 - 6x
= x2 - 6x + 5
= x2 - 5x - x + 5
= x(x - 5) - 1(x - 5)
= (x - 5)(x - 1)
= (3a2 - 2a - 5)(3a2 - 2a - 1)
= [3a2 - 5a + 3a - 5] [3a2 - 3a + a - 1]
= [a(3a - 5) + 1(3a - 5)] [3a(a - 1) + 1(a - 1)]
= (3a - 5)(a + 1)(a - 1)(3a + 1).
Hence, 5 - (3a2 - 2a)(6 - 3a2 + 2a) = (3a - 5)(a + 1)(a - 1)(3a + 1).