RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Mathematics

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Class 8 : RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev

The document RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev is a part of the Class 8 Course RD Sharma Solutions for Class 8 Mathematics.
All you need of Class 8 at this link: Class 8

Question 1: Divide the first polynomial by the second 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) x4x3 + 5x, x − 1
(v) y4 + y2, y2 − 2
Answer 1: 

(i) RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
(3x+10) RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
Therefore, quotient=3x+10 and remainder=25. (ii) RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
=(2x1/5)+ RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
Therefore,
quotient =2x−1/5 and remainder=47/5.
(iii) RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
=(y2−y+1)
Therefore, 

Quotient = y2−y+1 and remainder = 0
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev 
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
Therefore, quotient = x3+5 and remainder = 5. 
(v) RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
=(y2+3)+RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
Therefore, quotient = y2+3 and remainder = 6. 
Question 2: Find whether 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
Answer 2: 

(i) RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
=(2x+3)RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
∵ Remainder=1
Therefore, (x+1) is not a  factor of 2x2+5x+4
(ii) RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev 
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
=(3y2+11y+27)+ 56/y-2
∵ Remainder = 56

∴ (y−2) is not a factor of 3y3+5y2+5y+2.
(iii) RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
=(x2+3
)RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
∵ Remainder = 30

Therefore, (4x2−5) is not a factor of 4x4+7x2+15
(iv)
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
=1−3z
∵ Remainder = 0
∴ (4−z) is a factor of 3z2−13z+4.
(v) RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
=(5a+3)+ RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
∵ Remainder = 4

∴ ( 2a−3) is not a factor of 10a2−9a−5.
(vi) RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
=(2y−1) RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
∵ Remainder = 2

∴ (4y+1) is not a factor of 8y2−2y+1.
Question 3: Divide:
x2 − 5x + 6 by x − 3
Answer 3: 

RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
= x2 
Question 4:Divide:
ax2ay2 by ax + ay
Answer 4:

 RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
= xy 
Question 5: Divide:
x4y4 by x2y2
Answer 5:

 RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
= x2+y2 
Question 6: Divide:
acx2 + (bc + ad)x + bd by (ax + b)
Answer 6: 

RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
= cx+d 
Question 7: Divide:
(a2 + 2ab + b2) − (a2 + 2ac + c2) by 2a + b + c
Answer 7: 

RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
=bc 
Question 8: Divide: 
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
Answer 8: 

RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-3) Class 8 Notes | EduRev
=1/2 x+3 

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