In this section, we begin by exploring the division of a monomial by another monomial, which is a fundamental operation in algebra. We learn that division is the inverse operation of multiplication, and this relationship extends to algebraic expressions. By expressing both the dividend and the divisor in their irreducible factor forms, we can easily perform the division by canceling out common factors. For example, in the case of 6x³ divided by 2x, the process involves re-arranging the expression to allow for this cancellation, ultimately leading to a simplified expression. The section provides examples and explanations that illustrate how to carry out these operations effectively, laying the groundwork for further exploration of polynomial division.
Example: Do the following divisions.
(i) \(-30x^5 \div 10x^3\)
(ii) \(12a^3b^2c \div 4abc^3\)
Solution:
(i) \(-30x^5 \div 10x^3 = -3 \times 3 \times 2 \div 1 \times 1 \times 2 \times x^{5-3} = -3x^2\)
(ii) \(12a^3b^2c \div 4abc^3 = 3 \times 1 \times b^{2-1} \times a^{3-1} \times c^{1-3} = 3ab \div c^2\)
Therefore,
\(-30x^5 \div 10x^3 = -3x^2\) and \(12a^3b^2c \div 4abc^3 = 3abc^{-2}\)