Factoring Polynomials: Sum and Difference Formulas
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Factoring Polynomials: Sum and Difference Formulas

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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 $(x + 3)(x - 3)$

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    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.

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