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Algebra 1 Fundamentals: Polynomials Flashcards
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Algebra 1 Fundamentals: Polynomials Flashcards

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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?

<p>A term or a sum of terms whose variables have whole number exponents.</p> Signup and view all the answers

What defines a term in algebra?

<p>A number or a variable, or an indicated product of a number and variable(s).</p> Signup and view all the answers

What is a three-term polynomial called?

<p>trinomial</p> Signup and view all the answers

What is the polynomial $a^2 + bcd^3$ classified as?

<p>binomial</p> Signup and view all the answers

What is the polynomial $a^2 + b - cd^3$ classified as?

<p>trinomial</p> Signup and view all the answers

What is the classification of the polynomial $a^2 - b + c - d^3$?

<p>four-term polynomial</p> Signup and view all the answers

Order the polynomial -$x^4y^2 + 7x^3y^3 - 3xy^5 + 2x^2y^4$ in descending powers of x.

<p>-$x^4y^2$, +$7x^3y^3$, +$2x^2y^4$, and -$3xy^5$</p> Signup and view all the answers

Order the terms $p^2$, $p^4$, $p^3$, and $p$ in descending powers of p.

<p>$p^4$, $p^3$, $p^2$, and $p$</p> Signup and view all the answers

What is the result of adding $7b + 3$, $-4b + 5$, and $-3b + 2$?

<p>10</p> Signup and view all the answers

What is the result of adding $3x^2 + 2x - 5$ and $-4 + 7x^2$?

<p>$10x^2 + 2x - 9$</p> Signup and view all the answers

What is the result of adding $2mn + 4n^2$ and $5m^2 - 7mn$?

<p>$5m^2 - 5mn + 4n^2$</p> Signup and view all the answers

What is the opposite of the polynomial $9 - 12n^2 + 4n^3 - 7n$ after arranging in descending powers?

<p>-$4n^3 + 12n^2 + 7n - 9$</p> Signup and view all the answers

What is -$8 + b^2$ reduced by $5 + b^2$?

<p>-13</p> Signup and view all the answers

What is the result of finding $x - y$ subtracted from 0?

<p>-x + y</p> Signup and view all the answers

What is the result of $a - 2b + 3c$ diminished by $a - 2b - 3c + d$?

<p>$6c - d$</p> Signup and view all the answers

What is the result of setting up the subtraction $-4 + 3a^2$ from $7a - a^2$?

<p>-$4a^2 + 7a + 4$</p> Signup and view all the answers

What is the result of reducing $7y + 2y^2 - 7$ by $3 - 4y$?

<p>$2y^2 + 11y - 10$</p> Signup and view all the answers

What is the result of setting up the subtraction $2p^2 + 3p - 4$ less $-2p^2 - 3p + 4$?

<p>$4p^2 + 6p - 8$</p> Signup and view all the answers

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.

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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.

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