Polynomials Operations and Factoring
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Questions and Answers

What is the step to combine polynomials in addition and subtraction?

  • Combine terms with different variables and coefficients
  • Combine terms with the same variable(s) and coefficient(s) (correct)
  • Combine all terms without considering variables or coefficients
  • Add or subtract coefficients without considering variables

    • What is the formula for the difference of squares?

  • a^2 - 2ab + b^2
  • a^2 + b^2
  • a^2 - b^2 (correct)
  • a^2 + 2ab + b^2

    • What is the result of multiplying (2x + 3) by (x + 4)?

  • 2x^2 + 11x + 12 (correct)
  • 2x^2 + 6x + 12
  • 2x^2 + 5x + 3
  • 2x^2 + 8x + 3x + 12

    • What is the first step in long division of polynomials?

    <p>Write the dividend and divisor</p> Signup and view all the answers

    What is the result of adding (2x^2 + 3x - 1) and (x^2 - 2x - 3)?

    <p>3x^2 + x - 4</p> Signup and view all the answers

    What is the process of expressing a polynomial as a product of simpler expressions?

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

    What is the type of factoring that involves finding the largest common factor of all terms?

    <p>Greatest Common Factor (GCF)</p> Signup and view all the answers

    What is the result of dividing (x^2 + 3x + 2) by (x + 1)?

    <p>x + 2</p> Signup and view all the answers

    Study Notes

    Polynomials

    Addition and Subtraction

    • To add or subtract polynomials, combine like terms:
      • Combine terms with the same variable(s) and coefficient(s)
      • Add or subtract coefficients, keeping the variable(s) the same
    • Example: (2x^2 + 3x - 1) + (x^2 - 2x - 3) = 3x^2 + x - 4

    Factoring

    • Factoring is the process of expressing a polynomial as a product of simpler expressions
    • Types of factoring:
      • Greatest Common Factor (GCF): factor out the largest common factor of all terms
      • Difference of Squares: a^2 - b^2 = (a + b)(a - b)
      • Sum and Difference: a^2 + 2ab + b^2 = (a + b)^2, a^2 - 2ab + b^2 = (a - b)^2
    • Example: x^2 + 5x + 6 = (x + 3)(x + 2)

    Multiplication

    • To multiply polynomials, use the distributive property:
      • Multiply each term in one polynomial by each term in the other polynomial
      • Combine like terms
    • Example: (2x + 3)(x + 4) = 2x^2 + 8x + 3x + 12 = 2x^2 + 11x + 12

    Long Division

    • Long division is a method for dividing a polynomial by another polynomial
    • Steps:
      1. Write the dividend (divisor) and divisor
      2. Divide the first term of the dividend by the first term of the divisor
      3. Multiply the result by the divisor and subtract from the dividend
      4. Repeat steps 2-3 until the remainder is 0 or the degree of the remainder is less than the degree of the divisor
    • Example: (x^2 + 3x + 2) ÷ (x + 1) = x + 2

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    Description

    Learn how to add, subtract, multiply and divide polynomials, as well as factoring techniques including Greatest Common Factor, Difference of Squares, and Sum and Difference. Practice problems and examples are provided.

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