Key Concepts in Algebra: Dividing by a Monomial

Study Notes

Key Concepts in Algebra: Dividing by a Monomial

Monomial: A polynomial consisting of a single term.
Polynomial: A mathematical expression made up of variables with whole number exponents, represented as one term or a sum of multiple terms.

Finding Quotients

Example 1: (4z^a + 2 \div (-8z^a - 2) = -\frac{1}{2}z^4)
Example 2: (8y^7 \div 4y^5 = 2y^2)
Example 3: (12a^3p^4 \div -2a^2p = -6ap^3)
Example 4: (22x^2y^2 \div 11x^2y^2 = 2)

Simplifying Expressions

Expression: ((8z - 10) \div (-2) + 5(z - 1) = z)
Expression: (7 - 3\left[\frac{(n^3 + 8n)}{-n} + 9n^2\right] = -24n^2 + 31)

Polynomial Division

Example: ((18x^5 + 6x^4 - 12x^3) \div 6x^2 = 3x^3 + x^2 - 2x)
Example: ((5x - 35y + 50) \div 5 = x - 7y + 10)
Example: ((x^2 - 4xy) \div x = x - 4y)

Click-and-Find Quotients

Example: (12x^ay^b \div (-6x^ay) = -2y^{b-1})
Example: (36m^5n^5 \div 12m^3 = 3m^2n^5)

General Rules for Division

To divide monomials, divide the coefficients and subtract the exponents of like bases.
To divide a polynomial by a monomial, divide each term of the polynomial individually by the monomial.

Description

This quiz focuses on the essential techniques for dividing by a monomial and simplifying polynomial expressions. You will explore various examples and practice problems that reinforce the process of finding quotients in algebra. Test your understanding of monomials and polynomials through engaging questions and examples.