Questions and Answers
What is a monomial?
What defines a polynomial?
What is the quotient of $4z^a + 2 ÷ (-8z^a - 2)$?
-1/2^z4
What is the quotient of $8y^7 ÷ 4y^5$?
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What is the quotient of $12a^3p^4 ÷ -2a^2p$?
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What is the quotient of $22x^2y^2 ÷ 11x^2y^2$?
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What is the simplified result of $(8z - 10) ÷ (-2) + 5(z - 1)$?
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What is the quotient of $(18x^5 + 6x^4 - 12x^3) ÷ 6x^2$?
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What is the simplified form of $7 - 3[(n^3 + 8n) ÷ (-n) + 9n^2]$?
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What is the quotient of $12x^ay^b ÷ (-6x^ay)$?
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What is the quotient of $-300x^5y^4 ÷ xy^2$?
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What is the quotient of $(5x - 35y + 50) ÷ 5$?
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What is the quotient of $(x^2 - 4xy) ÷ x$?
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What is the quotient of $36m^5n^5 ÷ (12m^3)$?
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What is the quotient of $-10d^4e^3f^5 ÷ 15d^2e^2f$?
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What is the key concept when dividing monomials?
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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.
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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.
