# CLASS-7ALGEBRAIC DIVISION TO POLYNOMIAL BY MONOMIAL

Division of a Polynomial by a Monomial

The quotient of the monomials = ( numerical quotient of their coefficient) X ( quotient of their literal coefficient)

To divide the polynomial by monomial, divide each term of the polynomial by the monomial and add the partial quotient.

When we divide a polynomial by another, you can check your answer by using the relation,

Dividend = Divisor X Quotient + Remainder

Divide each term of the polynomial by the monomial and then add all the partial quotients thus obtained –

Example –

1)    ( 25 x⁷y⁶ - 15 x⁵y⁷ ) ÷ 10 x⁴y⁵

25 x⁷y⁶                15 x⁵y⁷

=    --------------  -  --------------

10 x⁴y⁵                10 x⁴y⁵

5                          3

=    --------  x⁷⁻⁴ y⁶⁻⁵  -  --------   x⁵⁻⁴y⁷⁻⁵

2                          2

=   5/2  xy¹ - 3/2 x¹ y²

=   5/2 xᶟ y - 3/2 x y²             (Ans.)

2)    ( 45 x⁸ y⁵ - 30 x⁶ y⁷ ) ÷ 15 xᶟ y⁴

45 x⁸ y⁵               30 x⁶ y⁷

=    ---------------  -  -------------

15 x y⁴                15 x y⁴

45                           30

=    ---------   x⁸⁻ y⁵⁻⁴   -  ----------   x⁶⁻ y⁷⁻⁴

15                           15

=   3  x⁵ y¹ -  2 x y                (Ans.)