Notes On Division of Algebraic Expressions - CBSE Class 8 Maths
In case of numbers Division is the inverse operation of multiplication but the same is applicable for the division of algebraic expressions also.

Division of a monomial by another monomial
To divide a monomial by a monomial, first express the numerator and the denominator in their irreducible form, and then cancel the common factors.

Division of a polynomial by a monomial
To divide a polynomial by a monomial, either divide each term of the numerator by the denominator or factorise the numerator by the common factor method.

Division of a polynomial by a polynomial
To divide a polynomial by a polynomial, first factorise the numerator and the denominator by using the appropriate method and then cancel the common factors.

Dividend = Divisor × Quotient + Remainder.

Hint: Division is the inverse operation of multiplication.
          2x × (2x+3) = 4x2 + 6x, then
          (4x2 + 6x) ÷ 2x = (2x+3)

Summary

In case of numbers Division is the inverse operation of multiplication but the same is applicable for the division of algebraic expressions also.

Division of a monomial by another monomial
To divide a monomial by a monomial, first express the numerator and the denominator in their irreducible form, and then cancel the common factors.

Division of a polynomial by a monomial
To divide a polynomial by a monomial, either divide each term of the numerator by the denominator or factorise the numerator by the common factor method.

Division of a polynomial by a polynomial
To divide a polynomial by a polynomial, first factorise the numerator and the denominator by using the appropriate method and then cancel the common factors.

Dividend = Divisor × Quotient + Remainder.

Hint: Division is the inverse operation of multiplication.
          2x × (2x+3) = 4x2 + 6x, then
          (4x2 + 6x) ÷ 2x = (2x+3)

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