Divide and verify: Dividend = Divisor × quotient + remainder. m 2 - 3 m + 7 by m - 2

Given, the polynomial 8 x 3 - 6 x 2 + 10 x + 15 to be divided by 4 x + 1 m - 2 ) m 2 - 3 m + 7 ( m - 1 m 2 - 2 m - + - m + 7 - m + 2 + - 5 Verification: Dividend = Divisor × quotient + remainder LHS = m 2 - 3 m + 7 RHS = Divisor × quotient + remainder ⇒ m - 2 × m - 1 + 5 ⇒ m m - 1 - 2 m - 1 + 5 ⇒ m 2 - m - 2 m + 2 + 5 ⇒ m 2 - 3 m + 7 This means, dividend = divisor × quotient + remainder. Therefore, obtained quotient = m - 1 and remainder = 5 , is correct.

Divide and verify: Dividend = Divisor × quotient + remainder. a 3 - 2 a 2 + a + 2 by a + 2

Given, the polynomial a 3 - 2 a 2 + a + 2 to be divided by a + 2 a + 2 ) a 3 - 2 a 2 + a + 2 ( a 2 - 4 a + 9 a 3 + 2 a 2 - - - 4 a 2 + a - 4 a 2 - 8 a + + 9 a + 2 9 a + 18 - - - 16 Verification: Dividend = Divisor × quotient + remainder LHS = a 3 - 2 a 2 + a + 2 RHS = Divisor × quotient + remainder ⇒ a + 2 × a 2 - 4 a + 9 - 16 ⇒ a a 2 - 4 a + 9 + 2 a 2 - 4 a + 9 - 16 ⇒ a 3 - 4 a 2 + 9 a + 2 a 2 - 8 a + 18 - 16 ⇒ a 3 - 2 a 2 + a + 2 This means, dividend = divisor × quotient + remainder. Therefore, obtained quotient = a 2 - 4 a + 9 and remainder = - 16 , is correct.

Divide and verify: Dividend = Divisor × quotient + remainder. 9 x 3 - 15 x 2 - 5 x + 3 by 3 x + 1

Given, the polynomial 9 x 3 - 15 x 2 - 5 x + 3 to be divided by 3 x + 1 3 x + 1 ) 9 x 3 - 15 x 2 - 5 x + 3 ( 3 x 2 - 6 x + 1 3 9 x 3 + 3 x 2 - - - 18 x 2 - 5 x - 18 x 2 - 6 x + + x + 3 x + 1 3 - - 8 3 Verification: Dividend = Divisor × quotient + remainder LHS = 9 x 3 - 15 x 2 - 5 x + 3 RHS = Divisor × quotient + remainder ⇒ 3 x + 1 × 3 x 2 - 6 x + 1 3 + 8 3 ⇒ 3 x 3 x 2 - 6 x + 1 3 + 1 3 x 2 - 6 x + 1 3 + 8 3 ⇒ 9 x 3 - 18 x 2 + x + 3 x 2 - 6 x + 1 3 + 8 3 ⇒ 9 x 3 - 15 x 2 - 5 x + 3 This means, dividend = divisor × quotient + remainder. Therefore, obtained quotient = 3 x 2 - 6 x + 1 3 and remainder = 8 3 , is correct.

Divide and verify: Dividend = Divisor × quotient + remainder. 2 x 3 + 3 x 2 + 7 x + 15 by x 2 + 4

Given, the polynomial 2 x 3 + 3 x 2 + 7 x + 15 to be divided by x 2 + 4 x 2 + 4 ) 2 x 3 + 3 x 2 + 7 x + 15 ( 2 x + 3 2 x 3 + 8 x - - + 3 x 2 - x + 15 3 x 2 + 12 + - - x + 3 Verification: Dividend = Divisor × quotient + remainder LHS = 2 x 3 + 3 x 2 + 7 x + 15 RHS = Divisor × quotient + remainder ⇒ x 2 + 4 × 2 x + 3 - x + 3 ⇒ x 2 2 x + 3 + 4 2 x + 3 - x + 3 ⇒ 2 x 3 + 3 x 2 + 8 x + 12 - x + 3 ⇒ 2 x 3 + 3 x 2 + 7 x + 15 This means, dividend = divisor × quotient + remainder. Therefore, obtained quotient = 2 x + 3 and remainder = - x + 3 , is correct.

E M B I B E

Mathematics Class - VIII>Chapter 4 - Multiplication & Division of Algebraic Expressions>EXERCISE 4.3

Chhattisgarh Board Solutions for Chapter: Multiplication & Division of Algebraic Expressions, Exercise 8: EXERCISE 4.3

Author:Chhattisgarh Board

Chhattisgarh Board Mathematics Solutions for Exercise - Chhattisgarh Board Solutions for Chapter: Multiplication & Division of Algebraic Expressions, Exercise 8: EXERCISE 4.3

Attempt the practice questions on Chapter 4: Multiplication & Division of Algebraic Expressions, Exercise 8: EXERCISE 4.3 with hints and solutions to strengthen your understanding. Mathematics Class - VIII solutions are prepared by Experienced Embibe Experts.