Algebra: Adding and Subtracting Polynomials
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Questions and Answers

What is the first step in adding polynomials?

  • Combine terms with different variables and exponents
  • Subtract the coefficients of the polynomials
  • Add the coefficients of the polynomials
  • Combine terms with the same variable(s) and exponent(s) (correct)
  • What is the result of adding $(2x^2 + 3x - 1)$ and $(x^2 - 2x - 3)$?

  • $3x^2 + x - 4$ (correct)
  • $2x^2 + x^2 + x - 4$
  • $3x^2 + 5x - 2$
  • $x^2 + 2x + 2$
  • How do you subtract polynomials?

  • Combine unlike terms and subtract coefficients
  • Combine like terms and add coefficients
  • Combine like terms and subtract coefficients (correct)
  • Combine unlike terms and add coefficients
  • What is the result of subtracting $(x^2 - 2x - 3)$ from $(2x^2 + 3x - 1)$?

    <p>$x^2 + 5x - 2$</p> Signup and view all the answers

    What is the purpose of combining like terms in polynomial operations?

    <p>To simplify the polynomial</p> Signup and view all the answers

    Study Notes

    Polynomial Operations

    Adding Polynomials

    • To add polynomials, combine like terms:
      • Combine terms with the same variable(s) and exponent(s)
      • Add the coefficients of the like terms
    • Example: (2x2+3x−1)+(x2−2x−3)=(2x2+x2)+(3x−2x)+(−1−3)=3x2+x−4(2x^2 + 3x - 1) + (x^2 - 2x - 3) = (2x^2 + x^2) + (3x - 2x) + (-1 - 3) = 3x^2 + x - 4(2x2+3x−1)+(x2−2x−3)=(2x2+x2)+(3x−2x)+(−1−3)=3x2+x−4

    Subtracting Polynomials

    • To subtract polynomials, combine like terms:
      • Change the sign of the terms in the second polynomial (i.e., subtract)
      • Combine terms with the same variable(s) and exponent(s)
      • Add the coefficients of the like terms
    • Example: (2x2+3x−1)−(x2−2x−3)=(2x2−x2)+(3x+2x)+(−1+3)=x2+5x+2(2x^2 + 3x - 1) - (x^2 - 2x - 3) = (2x^2 - x^2) + (3x + 2x) + (-1 + 3) = x^2 + 5x + 2(2x2+3x−1)−(x2−2x−3)=(2x2−x2)+(3x+2x)+(−1+3)=x2+5x+2

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    Description

    Learn how to add and subtract polynomials by combining like terms, including changing the sign of terms when subtracting. Practice with examples to become proficient in polynomial operations.

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