In the previous exercise, we have seen that the long division method is quite lengthy and time-consuming. In Exercise 8.5 of RD Sharma Solutions for Class 8 Maths Chapter 8 Division of Algebraic Expressions, we will explain an alternative form of the long division method. This form is concise and easy to use. The RD Sharma Solutions is prepared by the expert faculty at BYJU’S, which is one of the best reference materials, and also helps students to have a strong command over the subject to score well in their exams. Students can download the solutions in PDF from the links given below.
RD Sharma Solutions for Class 8 Maths Exercise 8.5 Chapter 8 Division of Algebraic Expressions
Access Answers to RD Sharma Solutions for Class 8 Maths Exercise 8.5 Chapter 8 Division of Algebraic Expressions
EXERCISE 8.5 PAGE NO: 8.15
1. Divide the first polynomial by the second polynomial in each of the following. Also, write the quotient and remainder:
(i) 3x2 + 4x + 5, x – 2
(ii) 10x2 – 7x + 8, 5x – 3
(iii) 5y3 – 6y2 + 6y – 1, 5y – 1
(iv) x4 – x3 + 5x, x – 1
(v) y4 + y2, y2 – 2
Solution:
(i) 3x2 + 4x + 5, x – 2
By using the long division method
∴ the Quotient is 3x + 10 and the remainder is 25.
(ii) 10x2 – 7x + 8, 5x – 3
By using the long division method
∴ the Quotient is 2x – 1/5 and the remainder is 37/5.
(iii) 5y3 – 6y2 + 6y – 1, 5y – 1
By using the long division method
∴ the Quotient is y2 – y + 1 and the remainder is 0.
(iv) x4 – x3 + 5x, x – 1
By using the long division method
∴ the Quotient is x3 + 5 and the remainder is 5.
(v) y4 + y2, y2 – 2
By using the long division method
∴ the Quotient is y2 + 3 and the remainder is 6.
2. Find whether or not the first polynomial is a factor of the second:
(i) x + 1, 2x2 + 5x + 4
(ii) y – 2, 3y3 + 5y2 + 5y + 2
(iii) 4x2 – 5, 4x4 + 7x2 + 15
(iv) 4 – z, 3z2 – 13z + 4
(v) 2a – 3, 10a2 – 9a – 5
(vi) 4y + 1, 8y2 – 2y + 1
Solution:
(i) x + 1, 2x2 + 5x + 4
Let us perform long division method,
Since the remainder is 1, the first polynomial is not a factor of the second polynomial.
(ii) y – 2, 3y3 + 5y2 + 5y + 2
Let us perform long division method,
Since the remainder is 56, the first polynomial is not a factor of the second polynomial.
(iii) 4x2 – 5, 4x4 + 7x2 + 15
Let us perform long division method,
Since the remainder is 30, the first polynomial is not a factor of the second polynomial.
(iv) 4 – z, 3z2 – 13z + 4
Let us perform long division method,
Since the remainder is 0, the first polynomial is a factor of the second polynomial.
(v) 2a – 3, 10a2 – 9a – 5
Let us perform long division method,
Since the remainder is 4, the first polynomial is not a factor of the second polynomial.
(vi) 4y + 1, 8y2 – 2y + 1
Let us perform long division method,
Since the remainder is 2, the first polynomial is not a factor of the second polynomial.
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