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
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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.
