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Questions and Answers
What is a monomial?
What is a monomial?
- A two-term polynomial
- A polynomial with variables
- A one-term polynomial (correct)
- A multi-variable equation
What defines a polynomial?
What defines a polynomial?
- A term or a sum of terms with whole number exponents (correct)
- Any algebraic expression
- A single term
- A term with negative exponents
What is the quotient of $4z^a + 2 ÷ (-8z^a - 2)$?
What is the quotient of $4z^a + 2 ÷ (-8z^a - 2)$?
-1/2^z4
What is the quotient of $8y^7 ÷ 4y^5$?
What is the quotient of $8y^7 ÷ 4y^5$?
What is the quotient of $12a^3p^4 ÷ -2a^2p$?
What is the quotient of $12a^3p^4 ÷ -2a^2p$?
What is the quotient of $22x^2y^2 ÷ 11x^2y^2$?
What is the quotient of $22x^2y^2 ÷ 11x^2y^2$?
What is the simplified result of $(8z - 10) ÷ (-2) + 5(z - 1)$?
What is the simplified result of $(8z - 10) ÷ (-2) + 5(z - 1)$?
What is the quotient of $(18x^5 + 6x^4 - 12x^3) ÷ 6x^2$?
What is the quotient of $(18x^5 + 6x^4 - 12x^3) ÷ 6x^2$?
What is the simplified form of $7 - 3[(n^3 + 8n) ÷ (-n) + 9n^2]$?
What is the simplified form of $7 - 3[(n^3 + 8n) ÷ (-n) + 9n^2]$?
What is the quotient of $12x^ay^b ÷ (-6x^ay)$?
What is the quotient of $12x^ay^b ÷ (-6x^ay)$?
What is the quotient of $-300x^5y^4 ÷ xy^2$?
What is the quotient of $-300x^5y^4 ÷ xy^2$?
What is the quotient of $(5x - 35y + 50) ÷ 5$?
What is the quotient of $(5x - 35y + 50) ÷ 5$?
What is the quotient of $(x^2 - 4xy) ÷ x$?
What is the quotient of $(x^2 - 4xy) ÷ x$?
What is the quotient of $36m^5n^5 ÷ (12m^3)$?
What is the quotient of $36m^5n^5 ÷ (12m^3)$?
What is the quotient of $-10d^4e^3f^5 ÷ 15d^2e^2f$?
What is the quotient of $-10d^4e^3f^5 ÷ 15d^2e^2f$?
What is the key concept when dividing monomials?
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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