NCERT Solutions for Class 8 Maths Chapter 8 Division Of Algebraic Expressions are provided here with simple step-by-step explanations. These solutions for Division Of Algebraic Expressions are extremely popular among class 8 students for Maths Division Of Algebraic Expressions Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the NCERT Book of class 8 Maths Chapter 8 are provided here for you for free. You will also love the ad-free experience on Meritnation’s NCERT Solutions. All NCERT Solutions for class 8 Maths are prepared by experts and are 100% accurate.
Page No 8.11:
Question 1:
Divide 5x3 − 15x2 + 25x by 5x.
Answer:
Page No 8.11:
Question 2:
Divide 4z3 + 6z2 − z by − z.
Answer:
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Question 3:
Divide 9x2y − 6xy + 12xy2 by −xy.
Answer:
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Question 4:
Divide 3x3y2 + 2x2y + 15xy by 3xy.
Answer:
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Question 5:
Divide x2 + 7x + 12 by x + 4.
Answer:
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Question 6:
Divide 4y2 + 3y + by 2y + 1.
Answer:
Page No 8.11:
Question 7:
Divide 3x3 + 4x2 + 5x + 18 by x + 2.
Answer:
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Question 8:
Divide 14x2 − 53x + 45 by 7x − 9.
Answer:
Page No 8.11:
Question 9:
Divide −21 + 71x − 31x2 − 24x3 by 3 − 8x.
Answer:
Page No 8.11:
Question 10:
Divide 3y4 − 3y3 − 4y2 − 4y by y2 − 2y.
Answer:
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Question 11:
Divide 2y5 + 10y4 + 6y3 + y2 + 5y + 3 by 2y3 + 1.
Answer:
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Question 12:
Divide x4 − 2x3 + 2x2 + x + 4 by x2 + x + 1.
Answer:
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Question 13:
Divide m3 − 14m2 + 37m − 26 by m2 − 12m +13.
Answer:
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Question 14:
Divide x4 + x2 + 1 by x2 + x + 1.
Answer:
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Question 15:
Divide x5 + x4 + x3 + x2 + x + 1 by x3 + 1.
Answer:
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Question 16:
Divide 14x3 − 5x2 + 9x − 1 by 2x − 1 and find the quotient and remainder
Answer:
Page No 8.11:
Question 17:
Divide 6x3 − x2 − 10x − 3 by 2x − 3 and find the quotient and remainder.
Answer:
Page No 8.11:
Question 18:
Divide 6x3+ 11x2 − 39x − 65 by 3x2 + 13x + 13 and find the quotient and remainder.
Answer:
Page No 8.12:
Question 19:
Divide 30x4 + 11x3 − 82x2 − 12x + 48 by 3x2 + 2x − 4 and find the quotient and remainder.
Answer:
Page No 8.12:
Question 20:
Divide 9x4 − 4x2 + 4 by 3x2 − 4x + 2 and find the quotient and remainder.
Answer:
Page No 8.12:
Question 21:
Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.
Dividend | Divisor | |
(i) | 14x2 + 13x − 15 | 7x − 4 |
(ii) | 15z3 − 20z2 + 13z − 12 | 3z − 6 |
(iii) | 6y5 − 28y3 + 3y2 + 30y − 9 | 2y2 − 6 |
(iv) | 34x − 22x3 − 12x4 − 10x2 − 75 | 3x + 7 |
(v) | 15y4 − 16y3 + 9y2 − y + 6 | 3y − 2 |
(vi) | 4y3 + 8y + 8y2 + 7 | 2y2 − y + 1 |
(vii) | 6y5 + 4y4 + 4y3 + 7y2 + 27y + 6 | 2y3 + 1 |
Answer:
(i)
Quotient = 2x + 3
Remainder = 3
Divisor = 7x 4
Divisor Quotient + Remainder = (7x 4) (2x + 3) â3
= 14x2 + 21x 8x 12 â3
= 14x2 + 13x 15
= Dividend
Thus,
Divisor Quotient + Remainder = Dividend
Hence verified.
(ii)
Hence verified.
(iii)
Quotient =
Remainder = 0
Divisor = 2y2 6
Divisor Quotient + Remainder =
= Dividend
Thus, Divisor Quotient + Remainder = Dividend
Hence verified.
(iv)
Quotient = 4x3 + 2x2 8x + 30
Remainder = 285
Divisor = 3x + 7
Divisor Quotient + Remainder = (3x + 7) ( 4x3 + 2x2 8x + 30) 285
= 12x4 + 6x3 24x2 + 90x 28x3 + 14x2 56x + 210 â285
= 12x 4 22x3 10x2 + 34x 75
= Dividend
Thus,
Divisor Quotient + Remainder = Dividend
Hence verified.
(v)
Quotient =
Remainder = 6
Divisor = 3y 2
Divisor Quotient + Remainder = (3y 2) (5y3 2y2 + ) + 6
=
=
= Dividend
Thus,
Divisor Quotient + Remainder = Dividend
Hence verified.
(vi)
Quotient = 2y + 5
Remainder = 11y + 2
Divisor = 2y2 y + 1
Divisor Quotient + Remainder = (2y2 y + 1) (2y + 5) + 11y + 2
= 4y3 +10y2 2y2 5y + 2y + 5 + 11y + 2
= 4y3 + 8y2 + 8y + 7
= Dividend
Thus,
Divisor Quotient + Remainder = Dividend
Hence verified.
(vii)
Quotient = 3y2 + 2y + 2
Remainder = 4y2 + 25y + 4
Divisor = 2y3 + 1
Divisor Quotient + Remainder = (2y3 + 1) (3y2 + 2y + 2) + 4y2 + 25y + 4
= 6y5 + 4y4 + 4y3 + 3y2 + 2y + 2 + 4y2 + 25y + 4
= 6y5 + 4y4 + 4y3 + 7y2 + 27y + 6
= Dividend
Thus,
Divisor Quotient + Remainder = Dividend
Hence verified.
Page No 8.12:
Question 22:
Divide 15y4 + 16y3 + y − 9y2 − 6 by 3y − 2. Write down the coefficients of the terms in the quotient.
Answer:
Quotient =
Coefficient
Page No 8.12:
Question 23:
Using division of polynomials, state whether
(i) x + 6 is a factor of x2 − x − 42
(ii) 4x − 1 is a factor of 4x2 − 13x − 12
(iii) 2y − 5 is a factor of 4y4 − 10y3 − 10y2 + 30y − 15
(iv) 3y2 + 5 is a factor of 6y5 + 15y4 + 16y3 + 4y2 + 10y − 35
(v) z2+ 3 is a factor of z5 − 9z
(vi) 2x2 − x + 3 is a factor of 6x5 − x4 + 4x3 − 5x2 − x − 15
Answer:
Remainder is zero. Hence (x+6) is a factor of x2 -x-42
(ii)
As the remainder is non zero . Hence ( 4x-1) is not a factor of 4x2 -13x-12
(iii)
The remainder is non zero,
2y 5 is not a factor of .
Remainder is zero. Therefore, 3y2 + 5 is a factor of .
Remainder is zero; therefore, z2 + 3 is a factor of .
Remainder is zero ; therefore, is a factor of .
Page No 8.12:
Question 24:
Find the value of a, if x + 2 is a factor of 4x4 + 2x3 − 3x2 + 8x + 5a.
Answer:
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Question 25:
What must be added to x4 + 2x3 − 2x2 + x − 1 , so that the resulting polynomial is exactly divisible by x2+ 2x − 3?
Answer:
Thus, (x 2) should be added to () to make the resulting polynomial exactly divisible by ().
Page No 8.15:
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) x4 − x3 + 5x, x − 1
(v) y4 + y2, y2 − 2
Answer:
Page No 8.15:
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:
Page No 8.17:
Question 1:
Divide:
x2 − 5x + 6 by x − 3
Answer:
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Question 2:
Divide:
ax2 − ay2 by ax + ay
Answer:
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Question 3:
Divide:
x4 − y4 by x2 − y2
Answer:
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Question 4:
Divide:
acx2 + (bc + ad)x + bd by (ax + b)
Answer:
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Question 5:
Divide:
(a2 + 2ab + b2) − (a2 + 2ac + c2) by 2a + b + c
Answer:
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Question 6:
Divide:
Answer:
Page No 8.2:
Question 1:
Write the degree of each of the following polynomials.
(i) 2x2 + 5x2 − 7
(ii) 5x2 − 3x + 2
(iii) 2x + x2 − 8
(iv)
(v) 3x3 + 1
(vi) 5
(vii) 20x3 + 12x2y2 − 10y2 + 20
Answer:
Page No 8.2:
Question 2:
Which of the following expressions are not polynomials?
(i) x2 + 2x−2
(ii)
(iii) 3y3 − + 9
(iv) ax1/2 + ax + 9x2 + 4
(v) 3x−2 + 2x−1 + 4x +5
Answer:
Page No 8.2:
Question 3:
Write each of the following polynomials in the standard form. Also, write their degree.
(i) x2 + 3 + 6x + 5x4
(ii) a2 + 4 + 5a6
(iii) (x3 − 1)(x3 − 4)
(iv) (y3− 2)(y3+ 11)
(v)
(vi)
Answer:
Page No 8.4:
Question 1:
Divide 6x3y2z2 by 3x2yz.
Answer:
Page No 8.4:
Question 2:
Divide 15m2n3 by 5m2n2.
Answer:
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Question 3:
Divide 24a3b3 by −8ab.
Answer:
Page No 8.4:
Question 4:
Divide −21abc2 by 7abc.
Answer:
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Question 5:
Divide 72xyz2 by −9xz.
Answer:
â
Page No 8.4:
Question 6:
Divide −72a4b5c8 by −9a2b2c3.
Answer:
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Question 7:
Simplify:
Answer:
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Question 8:
Simplify:
Answer:
Page No 8.6:
Question 1:
Divide x + 2x2 + 3x4 − x5 by 2x.
Answer:
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Question 2:
Divide .
Answer:
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Question 3:
Divide −4a3 + 4a2 + a by 2a.
Answer:
Page No 8.6:
Question 4:
Divide .
Answer:
Page No 8.6:
Question 5:
Divide 5z3 − 6z2 + 7z by 2z.
Answer:
Page No 8.6:
Question 6:
Divide .
Answer:
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