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Questions and Answers
What is a two-term polynomial?
binomial
What are like terms?
Terms that have the same variable(s), with each variable raised to the same exponent.
What is a one term polynomial called?
monomial
What is a polynomial?
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What defines a term in algebra?
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What is a three-term polynomial called?
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What is the polynomial $a^2 + bcd^3$ classified as?
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What is the polynomial $a^2 + b - cd^3$ classified as?
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What is the classification of the polynomial $a^2 - b + c - d^3$?
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Order the polynomial -$x^4y^2 + 7x^3y^3 - 3xy^5 + 2x^2y^4$ in descending powers of x.
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Order the terms $p^2$, $p^4$, $p^3$, and $p$ in descending powers of p.
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What is the result of adding $7b + 3$, $-4b + 5$, and $-3b + 2$?
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What is the result of adding $3x^2 + 2x - 5$ and $-4 + 7x^2$?
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What is the result of adding $2mn + 4n^2$ and $5m^2 - 7mn$?
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What is the opposite of the polynomial $9 - 12n^2 + 4n^3 - 7n$ after arranging in descending powers?
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What is -$8 + b^2$ reduced by $5 + b^2$?
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What is the result of finding $x - y$ subtracted from 0?
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What is the result of $a - 2b + 3c$ diminished by $a - 2b - 3c + d$?
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What is the result of setting up the subtraction $-4 + 3a^2$ from $7a - a^2$?
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What is the result of reducing $7y + 2y^2 - 7$ by $3 - 4y$?
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What is the result of setting up the subtraction $2p^2 + 3p - 4$ less $-2p^2 - 3p + 4$?
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Study Notes
Polynomials Overview
- A binomial consists of two terms.
- Like terms share the same variable(s) and exponents.
- A monomial is defined as a single-term polynomial.
- A polynomial can be one term or the sum of multiple terms with whole number exponents.
- A term can be a number, a variable, or a product of numbers and variables.
- A trinomial is a polynomial containing three terms.
Examples of Polynomials
- a² + bcd³ is classified as a binomial.
- a² + b - cd³ identifies as a trinomial.
- a² - b + c - d³ represents a four-term polynomial.
Ordering Polynomials
- To arrange -x⁴y² + 7x³y³ - 3xy⁵ + 2x²y⁴ in descending powers of x:
- Order: -x⁴y², +7x³y³, +2x²y⁴, -3xy⁵.
- To order terms p², p⁴, p³, and p in descending powers of p:
- Order: p⁴, p³, p², p.
Polynomial Operations
- Simplifying 7b + 3, -4b + 5, and -3b + 2 results in a total of 10.
- Adding 3x² + 2x - 5 and -4 + 7x² gives:
- Result: 10x² + 2x - 9.
- Combining 2mn + 4n² and 5m² - 7mn yields:
- Result: 5m² - 5mn + 4n².
Subtraction in Polynomials
- The opposite of 9 - 12n² + 4n³ - 7n after ordering is:
- Result: -4n³ + 12n² + 7n - 9.
- Reducing -8 + b² by 5 + b² results in:
- Answer: -13.
- Finding x - y subtracted from 0 gives:
- Answer: -x + y.
Complex Subtractions
- The expression a - 2b + 3c diminished by a - 2b - 3c + d results in:
- Answer: 6c - d.
- For the operation of -4 + 3a² taken from 7a - a²:
- Set up vertically yields: -4a² + 7a + 4.
- Reducing 7y + 2y² - 7 by 3 - 4y leads to:
- Result: 2y² + 11y - 10.
- For 2p² + 3p - 4 less -2p² - 3p + 4:
- Result: 4p² + 6p - 8.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge of polynomials with these flashcards focusing on key terms in Algebra 1. Learn about binomials, monomials, and like terms in a concise manner. Perfect for quick study sessions and review of polynomial basics.