Factoring Polynomials: Sum and Difference Formulas
5 Questions
0 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the formula for the sum of cubes?

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

    • What is the first step in factoring out the greatest common factor (GCF) of a polynomial?

  • Divide each term by the GCF
  • Factor out the GCF from each term
  • Write the result as a product of the GCF and the remaining terms
  • Find the GCF of all terms (correct)

    • What is the formula for the difference of squares?

  • $(a - b)(a + b)$
  • $(a + b)(a + b)$
  • $(a - b)(a - b)$
  • $(a + b)(a - b)$ (correct)

    • What is the result of factoring out the GCF from the expression $6x^2 + 12x + 18$?

    <p>$6(x^2 + 2x + 3)$</p> Signup and view all the answers

    What is the result of factoring the expression $x^2 - 9$?

    <p>$(x + 3)(x - 3)$</p> Signup and view all the answers

    Study Notes

    Factoring Polynomials

    Sum and Difference Formulas

    • Sum of Cubes Formula: $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$
    • Difference of Cubes Formula: $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$

    Factoring Out Greatest Common Factors (GCF)

    • GCF: the largest number or expression that divides all terms of the polynomial
    • Steps to factor out the GCF:
      1. Find the GCF of all terms
      2. Divide each term by the GCF
      3. Write the result as a product of the GCF and the remaining terms

    Example: Factor $6x^2 + 12x + 18$ * GCF = 6 * Factor out 6: $6(x^2 + 2x + 3)$

    Difference of Squares

    • Difference of Squares Formula: $a^2 - b^2 = (a + b)(a - b)$
    • Factoring: $a^2 - b^2 = (a + b)(a - b)$
    • Example: Factor $x^2 - 9$
      • $x^2 - 9 = (x + 3)(x - 3)$

    Sum and Difference Formulas

    • The Sum of Cubes Formula is: $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$
    • The Difference of Cubes Formula is: $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$

    Factoring Out Greatest Common Factors (GCF)

    • The GCF is the largest number or expression that divides all terms of the polynomial
    • Steps to factor out the GCF are:
      • Find the GCF of all terms
      • Divide each term by the GCF
      • Write the result as a product of the GCF and the remaining terms
    • Example: Factoring $6x^2 + 12x + 18$ involves finding the GCF as 6, then writing it as $6(x^2 + 2x + 3)$

    Difference of Squares

    • The Difference of Squares Formula is: $a^2 - b^2 = (a + b)(a - b)$
    • Factoring $a^2 - b^2$ results in $(a + b)(a - b)$
    • Example: Factoring $x^2 - 9$ results in $(x + 3)(x - 3)$

    Studying That Suits You

    Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

    Quiz Team

    Description

    Solve polynomial equations using the sum and difference formulas, and learn how to factor out the greatest common factor (GCF) of a polynomial expression.

    More Like This

    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser