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 xᶟ y¹ - 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 xᶟ y⁴ 15 xᶟ y⁴
45 30
= --------- x⁸⁻ᶟ y⁵⁻⁴ - ---------- x⁶⁻ᶟ y⁷⁻⁴
15 15
= 3 x⁵ y¹ - 2 xᶟ yᶟ (Ans.)