Divide the given polynomial by the given monomial.
(i) (5x2 - 6x) ÷ 3x (ii) (3y8 - 4y6 + 5y4) ÷ y4
(iii) 8(x3y2z2 + x2y3z2 + x2y2z3) ÷ 4x2y2z2
(iv) (x3 + 2x2 + 3x) ÷ 2x (v) (p3q6 - p6q3) ÷ p3q3
Solution:
We will find out factors of the algebraic expression and then cancel out common factors of the numerator.
(i) (5x2 - 6x) ÷ 3x
(5x2 - 6x) can be written as x(5x - 6)
Then, (5x2 - 6x) ÷ 3x = x(5x - 6) / 3x
= (5x - 6) / 3
(ii) (3y8 - 4y6 + 5y4) ÷ y4
(3y8 - 4y6 + 5y4) can be written as y4(3y4 - 4y2 + 5)
Then, (3y8 - 4y6 + 5y4) ÷ y4 = y4(3y4 - 4y2 + 5) / y4
= 3y4 - 4y2 + 5
(iii) 8(x3y2z2 + x2y3z2 + x2y2z3) ÷ 4x2y2z2
8(x3y2z2 + x2y3z2 + x2y2z3) can be written as 8x2y2z2(x + y + z)
Then, 8(x3y2z2 + x2y3z2 + x2y2z3) ÷ 4x2y2z2 = 8x2y2z2(x + y + z) / 4x2y2z2
= 2(x + y + z)
(iv) (x3 + 2x2 + 3x) ÷ 2x
(x3 + 2x2 + 3x) can be written as x(x2 + 2x + 3)
Then, (x3 + 2x2 + 3x) ÷ 2x = x(x2 + 2x + 3) / 2x
= (x2 + 2x + 3) / 2
(v) (p3q6 - p6q3) ÷ p3q3
(p3q6 - p6q3) can be written as p3q3 (q3 - p3)
Then, (p3q6 - p6q3) ÷ p3q3= p3q3 (q3 - p3) / p3q3
= q3 - p3
☛ Check: NCERT Solutions for Class 8 Maths Chapter 14
Video Solution:
Divide the given polynomial by the given monomial. (i) (5x² - 6x) ÷ 3x (ii) (3y⁸ - 4y⁶ + 5y⁴) ÷ y⁴ (iii) 8(x³y²z² + x²y³z² + x²y²z³) ÷ 4x²y²z² (iv) (x³ + 2x² + 3x) ÷ 2x (v) (p³q⁶ - p⁶q³) ÷ p³q³
Class 8 Maths NCERT Solutions Chapter 14 Exercise 14.3 Question 2
Summary:
The given polynomial is divided by the given monomial. (i) (5x2 - 6x) ÷ 3x (ii) (3y8 - 4y6 + 5y4) ÷ y4 (iii) 8(x3y2z2 + x2y3z2 + x2y2z3) ÷ 4x2y2z2 (iv) (x3 + 2x2 + 3x) ÷ 2x (v) (p3q6 - p6q3) ÷ p3q3 and the results are (i) (5x - 6) / 3 (ii) 3y4 - 4y2 + 5 (iii) 2(x + y + z) (iv)(x2 + 2x + 3) / 2 (v) q3 - p3
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