AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3

AP State Syllabus AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3 Textbook Questions and Answers.

AP State Syllabus 8th Class Maths Solutions 12th Lesson Factorisation Exercise 12.3

AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3

Question 1.
Carry out the following divisions
(i) 48a3 by 6a
(ii) 14x3 by 42x3
(iii) 72a3b4c5 by 8ab2c3
(iv) 11xy2z3 by 55xyz
(v) -54l4m3n2 by 9l2m2n2
Solution:
(i) 48a3 by 6a
48a3 ÷ 6a
= \(\frac{6 \times 8 \times a \times a^{2}}{6 \times a}\)
= 8a2

(ii) 14x3 by 42x3
= 14x3 ÷ 42x3
AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3 1

AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3

(iii) 72a3b4c5 by 8ab2c3
AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3 2

(iv) 11xy2z3 by 55xyz
11xy2z3 ÷ 55xyz
AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3 3

(v) -54l4m3n2 by 9l2m2n2
-54l4m3n2 ÷ 9l2m2n2
AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3 4
= -6l2m

Question 2.
Divide the given polynomial by the given monomial
(i) (3x2 – 2x) ÷ x
(ii) (5a3b – 7ab3) ÷ ab
(iii) (25x5 – 15x4) ÷ 5x3
(iv) (4l5 – 6l4 + 8l3) ÷ 2l2
(v) 15 (a3b2c2 – a2b3c2 + a2b2c3 ) ÷ 3abc
(vi) 3p3– 9p2q – 6pq2) ÷ (-3p)
(vii) (\(\frac{2}{3}\) a2 b2 c2+ \(\frac{4}{3}\) a b2 c3) ÷ \(\frac{1}{2}\)abc
Solution:
(i) (3x2 – 2x) ÷ x
AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3 5

AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3

(ii) (5a3b – 7ab3) ÷ ab
AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3 6

(iii) (25x5 – 15x4) ÷ 5x3
AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3 7
= 5x2 – 3x (or) x(5x – 3)

(iv) (4l5 – 6l4 + 8l3) ÷ 2l2
AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3 8
= 2l2 – 3l2 + 4l = l(2l2 – 3l + 4)

(v) 15 (a3 b2 c2 – a2 b3 c2 + a2 b2 c3 ) ÷ 3abc
AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3 9
= 5[a x abc – b x abc + c x abc ]
= 5abc [a – b + c]

AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3

(vi) 3p3– 9p2q – 6pq2) ÷ (-3p)
AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3 10
= -[p2 – 3pq – 2q2]
= 22 + 3pq – p2

(vii) (\(\frac{2}{3}\) a2b2c2+ \(\frac{4}{3}\) ab2c3) ÷ \(\frac{1}{2}\)abc
AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3 11

AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3

Question 3.
Workout the following divisions:
(i) (49x -63) ÷ 7
(ii) 12x (8x – 20,) ÷ 4(2x – 5)
(iii) 11a3 b3 (7c – 35) ÷ 3a2 b2 (c – 5)
(iv) 54lmn (l + m) (m + n) (n + l) ÷ 8 lmn (l + m) (n +l)
(v) 36(x + 4)(x2 + 7x + 10) ÷ 9(x + 4)
(vi) a(a+1)(a+2)(a + 3) ÷ a(a + 3)
Solution:
(i) (49x -63) ÷ 7
AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3 12

(ii) 12x (8x – 20,) ÷ 4(2x – 5)
AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3 13

AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3

(iii) 11a3 b3 (7c – 35) ÷ 3a2 b2 (c – 5)
AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3 14

(iv) 54lmn (l + m) (m + n) (n + l) ÷ 8 lmn (l + m) (n +l)
AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3 15

(v) 36(x + 4)(x2 + 7x + 10) ÷ 9(x + 4)
AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3 16
4 ( x2 + 7x + 10)
= 4 ( x2 + 5x + 2x + 10)
= 4 [x( x + 5) +2(x + 5)]
= 4( x + 5) (x + 2)

(vi) a(a+1)(a+2)(a + 3) ÷ a(a + 3)
AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3 17
= ( a + 1)(a + 2)

AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3

Question 4.
Factorize the expressions and divide them as directed:
(i) (x2 + 7x + 12) ÷ (x + 3)
(ii) (x2 – 8x + 12) ÷ (x – 6)
(iii) (p2 + 5p + 4,) (p + l)
(iv) 15ab(a2 – 7a + 10) ÷ 3b(a – 2)
(v) 151m (2p2 – 2q2) ÷ 3l(p + q)
(vi) 26z3(32z2 – 18,) ÷ 13z2 (4z – 3)
Solution:
(i) (x2 + 7x + 12) ÷ (x + 3)
(x2 + 7x + 12) ÷ (x + 3)
x2 + 7x + 12 = x2 + 3x + 4x + 12
= x(x + 3) + 4(x + 3)
= (x + 3) (x + 4)
AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3 18

(ii) (x2 – 8x + 12) ÷ (x – 6)
(x2 – 8x + 12) ÷ (x – 6)
x2 – 8x + 12 = x2 – 6x – 2x + 12
= x(x – 6) – 2(x – 6)
= (x – 6) (x – 2)
∴ (x2 – 8x + 12) 4 (x – 6)
= \(\frac{(x-6)(x-2)}{(x-6)}\) = x – 2

AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3

(iii) (p2 + 5p + 4,) (p + 1)
p2 + 5p + 4 = p2 + p + 4p + 4
= p(p + 1) + 4(p + 1)
= (p + 1) (p + 4)
(p2 + 5p + 4) ÷ (p + 1)
= \(\frac{(p+1)(p+4)}{(p+1)}\) = p + 4

(iv) 15ab(a2 – 7a + 10) ÷ 3b(a – 2)
15ab (a2 – 7a + 10) ÷ 3b (a – 2)
15ab (a2 – 7a + 10) = 15ab (a2 – 5a – 2a + 10)
= 15ab [(a2 – 2a) – (5a -10)]
= 15ab [a(a – 2) – 5(a – 2)]
= 15ab(a – 2)(a – 5)
∴ 15ab (a2 – 7a + 10) ÷ 3b (a – 2)
AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3 19

(v) 151m (2p2 – 2q2) ÷ 3l(p + q)
15lm (2p2 – 2q2) ÷ 3l (p + q)
15lm (2p2 – 2q2) = 15lm x 2(p2 – q2)
= 30lm (p + q) (p – q)
∴ 15lm(2p2 – 2q2) ÷ 3l(p + q)
AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3 20

AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3

(vi) 26z3(32z2 – 18,) ÷ 13z2 (4z – 3)
26z3(32z2 – 18) ÷ 13z2 (4z – 3)
26z3(32z2 – 18) = 26z3 (2 x 16z2 – 2 x 9)
= 26z3 x 2 [16z3 – 9]
= 52z3 [(4z)3 – (3)3]
= 52z3 (4z + 3) (4z – 3)
∴ 26z3 (32z2 – 18) ÷ 13z2 (4z – 3)
AP Board 8th Class Maths Solutions Chapter 12 Factorisation Ex 12.3 21