R d sharma solutions mathematics class 8 Solutions for Chapter 8 division of algebraic expressions

Write the degree of each of the following polynomials:

(i) 2×3 + 5×2 -7

(ii) 5×2 – 3x + 2

(iii) 2x + x2 -8

(iv) 1/2y7 – 12y6 + 48y5 -10

(v) 3×3 + 1

(vi) 5

(vii) 20×3 + 12×2 y 2 – 10y2 + 20

Which of the following expressions are not polynomials?

(i) x2 + 2x-2

(ii) √(ax) + x2 – x 3

(iii) 3y3 -√5y + 9

(iv) ax1/2 + ax + 9×2 + 4

(v) 3x-3 + 2x-1 + 4x + 5

Write each of the following polynomials in the standard from. Also, write their degree:

(i) x2 + 3 + 6x + 5×4

(ii) a2 + 4 + 5a6

(iii) (x3 -1) (x3 -4)

(iv) (y3 -2) (y3 + 11)

(v) (a3 – 3/8) (a3 + 16/17) (vi) (a + 3/4) (a + 4/3)

Divide:

6x 3 y 2 z 2 by 3x 2 yz

Divide:

15m 2 n 3 by 5m 2 n 2

Divide:

24a 3 b 3 by -8ab

Divide:

-21abc 2 by 7abc

Divide:

72xyz 2 by -9xz

Divide:

-72a4 b5 c 8 by -9a2 b2 c 3

Simplify:

16m3 y 2 / 4m2 y

Simplify:

32m2 n3 p2 / 4mnp

Divide:

x + 2×2 + 3×4 – x 5 by 2x

Divide:

y4 – 3y3 + 1/2y2 by 3y

Divide:

-4a3 + 4a2 + a by 2a

Divide:

–x6 + 2×4 + 4×3 + 2×2 by √2×2

Divede:

-4a3 + 4a2 + a by 2a

Divide:

√3a4 + 2√3a3 + 3a2 – 6a by 3a

Divide:

5×3 – 15×2 + 25x by 5x

Divide:

4z3 + 6z2 – z by -1/2z

Divide:

9×2 y – 6xy + 12xy2 by -3/2xy

Divide:

3×3 y 2 + 2×2 y + 15xy by 3xy

Divide:

x 3 + 7x + 12 by x + 4

Divide:

4y2 + 3y + 1/2 by 2y + 1

Divide:

3×3 + 4×2 + 5x + 18 by x + 2

Divede:

14×2 – 53x + 45 by 7x – 9

Divide:

-21 + 71x – 31×2 – 24×3 by 3 – 8x

Divide:

3y4 – 3y3 – 4y2 – 4y by y2 -2y

Divide:

2y5 + 10y4 + 6y3 + y2 + 5y + 3 by 2y3 + 1

Divide:

x 4 – 2×3 + 2×2 + x + 4 by x2 + x + 1

Divide:

m3 – 14m2 + 37m – 26 by m2 – 12m + 13

Divide:

x4 + x2 + 1 by x2 + x + 1

Divide:

x5 + x4 + x3 + x2 + x + 1 by x3 + 1

Divide each of the following and find the quotient and remainder:

14×3 – 5×2 + 9x – 1 by 2x – 1

Divide each of the following and find the quotient and remainder:

6×3 – x 2 – 10x – 3 by 2x – 3

Divide each of the following and find the quotient and remainder:

6×3 + 11×2 – 39x – 65 by 3×2 + 13x + 13

Divide each of the following and find the quotient and remainder:

30×4 + 11×3 – 82×2 – 12x + 48 by 3×2 + 2x – 4

Divide each of the following and find the quotient and remainder:

9×4 – 4×2 + 4 by 3×2 – 4x + 2

Verify division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder: Dividend divisor

(i) 14×2 + 13x – 15 7x – 4

(ii) 15z3 – 20z2 + 13z – 12 3z – 6

(iii) 6y5 – 28y3 + 3y2 + 30y – 9 2×2 – 6

(iv) 34x – 22×3 – 12×4 – 10×2 – 75 3x + 7

(v) 15y4 – 16y3 + 9y2 – 10/3y + 6 3y – 2

(vi) 4y3 + 8y + 8y2 +7 2y2 – y + 1

(vii) 6y4 + 4y4 + 4y3 + 7y2 + 27y + 6 2y3 +1

Divide 15y4 +16y3 + 10/3y – 9y2 – 6 by 3y – 2 Write down the coefficients of the terms in the quotient.

Using division of polynomials state whether

(i) x + 6 is a factor of x2 – x – 42

(ii) 4x – 1 is a factor of 4×2 – 13x – 12

(iii) 2y – 5 is a factor of 4y4 – 10y3 – 10y2 + 30y – 15

(iv) 3y 2 + 5 is a factor of 6y5 + 15y4 + 16y3 + 4y2 + 10y – 35

(v) z 2 + 3 is a factor of z5 – 9z

(vi) 2×2 – x + 3 is a factor of 6×5 – x 4 + 4×3 – 5×2 – x – 15

Find the value of a, if x + 2 is a factor of 4×4 + 2×3 – 3×2 + 8x + 5a

What must be added to x4 + 2×3 – 2×2 + x – 1 so that the resulting polynomial is exactly divisible by x2 + 2x -3.

Divide the first polynomial by the second polynomial in each of the following. Also, write the quotient and remainder:

(i) 3x 2 + 4x + 5, x – 2

(ii) 10×2 – 7x + 8, 5x – 3

(iii) 5y 3 – 6y2 + 6y – 1, 5y – 1

(iv) x 4 – x 3 + 5x, x – 1

(v) y4 + y2 , y 2 – 2

Find Whether or not the first polynomial is a factor of the second:

(i) x + 1, 2×2 + 5x + 4

(ii) y – 2, 3y3 + 5y2 + 5y + 2

(iii) 4×2 – 5, 4×4 + 7×2 + 15

(iv) 4 – z, 3z2 – 13z + 4

(v) 2a – 3, 10a2 – 9a – 5

(vi) 4y + 1, 8y2 – 2y + 1

Divide:

x 2 – 5x + 6 by x – 3

Divide:

ax2 – ay2 by ax+ay

Divide:

x 4 – y 4 by x2 – y 2

Divide;

acx2 + (bc + ad)x + bd by (ax + b)

Divide:

(a2 + 2ab + b2 ) – (a2 + 2ac + c2 ) by 2a + b + c

Divide:

1/4×2 – 1/2x – 12 by 1/2x – 4