RD Sharma solutions for Mathematics [English] Class 8 chapter 8 - Division of Algebraic Expressions [Latest edition]

Write the degree of each of the following polynomials.
2x² + 5x² − 7 

Write the degree of each of the following polynomials.
5x² − 3x + 2

Write the degree of each of the following polynomials.
2x + x² − 8

Write the degree of each of the following polynomials.

Write the degree of each of the following polynomials.

Write the degree of each of the following polynomials.

Write the degree of each of the following polynomials.

Which of the following expressions are not polynomials?

 x² + 2x⁻²

Which of the following expressions are not polynomials?

Which of the following expressions are not polynomials?

Which of the following expressions are not polynomials?

Which of the following expressions are not polynomials?

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

x² + 3 + 6x + 5x⁴

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

 a² + 4 + 5a⁶

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

(x³ − 1)(x³ − 4)

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

(y³ − 2)(y³ + 11)

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

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

Simplify:\[\frac{16 m^3 y^2}{4 m^2 y}\]

Simplify:\[\frac{32 m^2 n^3 p^2}{4mnp}\]

Divide \[y^4 - 3 y^3 + \frac{1}{2} y^2 by 3y\]

Divide\[- x^6 + 2 x^4 + 4 x^3 + 2 x^2\ \text{by} \sqrt{2} x^2\]

Divide\[\sqrt{3} a^4 + 2\sqrt{3} a^3 + 3 a^2 - 6a\ \text{by}\ 3a\]

Divide 4z³ + 6z² − z by −\[\frac{1}{2}\]

Divide 9x²y − 6xy + 12xy² by −\[\frac{3}{2}\]

Divide 4y² + 3y +\[\frac{1}{2}\] by 2y + 1.

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

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

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

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

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

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

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

Divide 15y⁴ + 16y³ +\[\frac{10}{3}\]y − 9y² − 6 by 3y − 2. Write down the coefficients of the terms in the quotient.

Using division of polynomials, state whether

x + 6 is a factor of  x² − x − 42

Using division of polynomials, state whether

 4x − 1 is a factor of 4x² − 13x − 12

Using division of polynomials, state whether

2y − 5 is a factor of 4y⁴ − 10y³ − 10y² + 30y − 15

Using division of polynomials, state whether

3y² + 5 is a factor of 6y⁵ + 15y⁴ + 16y³ + 4y² + 10y − 35

Using division of polynomials, state whether

z² + 3 is a factor of z⁵ − 9z

Using division of polynomials, state whether

2x² − x + 3 is a factor of 6x⁵ − x⁴ + 4x³ − 5x² − x − 15

What must be added to x⁴ + 2x³ − 2x² + x − 1 , so that the resulting polynomial is exactly divisible by x² + 2x − 3?

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

3x² + 4x + 5, x − 2

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

 10x² − 7x + 8, 5x − 3

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

5y³ − 6y² + 6y − 1, 5y − 1

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

 x⁴ − x³ + 5x, x − 1

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

y⁴ + y², y² − 2

Find whether the first polynomial is a factor of the second.

x + 1, 2x² + 5x + 4

Find whether the first polynomial is a factor of the second.

y − 2, 3y³ + 5y² + 5y + 2

Find whether the first polynomial is a factor of the second.

 4x² − 5, 4x⁴ + 7x² + 15

Find whether the first polynomial is a factor of the second.

 4 − z, 3z² − 13z + 4

Find whether the first polynomial is a factor of the second.

2a − 3, 10a² − 9a − 5

Find whether the first polynomial is a factor of the second.

4y + 1, 8y² − 2y + 1

Divide:
x² − 5x + 6 by x − 3

Divide:
ax² − ay² by ax + ay

Divide:
x⁴ − y⁴ by x² − y²

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

Divide:

Divide: