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Factoring Special Products quiz

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Terms in this set (15)

  • What is the formula for factoring a difference of squares?
    The formula is a^2 - b^2 = (a + b)(a - b).
  • What criteria must be met to use the difference of squares factoring rule?
    Both terms must be perfect squares and have opposite signs.
  • How would you factor x^2 - 4 using the difference of squares rule?
    It factors as (x + 2)(x - 2).
  • Can a sum of squares, like a^2 + b^2, be factored using the difference of squares rule?
    No, a sum of squares cannot be factored using this rule.
  • How do you factor 16 - 9x^2 using the difference of squares?
    It factors as (4 + 3x)(4 - 3x).
  • What is a perfect square trinomial and how is it factored?
    A perfect square trinomial has first and last terms as perfect squares and the middle term as 2ab; it factors as (a ± b)^2.
  • How do you factor x^2 + 10x + 25 as a perfect square trinomial?
    It factors as (x + 5)^2.
  • What must the middle term of a perfect square trinomial equal for factoring?
    The middle term must equal 2ab, where a and b are the square roots of the first and last terms.
  • How do you factor 4x^2 - 36x + 81 as a perfect square trinomial?
    It factors as (2x - 9)^2.
  • What determines whether you use (a + b)^2 or (a - b)^2 when factoring a perfect square trinomial?
    The sign of the middle term determines whether you use plus or minus.
  • What is the formula for factoring a sum of cubes?
    a^3 + b^3 = (a + b)(a^2 - ab + b^2).
  • What is the formula for factoring a difference of cubes?
    a^3 - b^3 = (a - b)(a^2 + ab + b^2).
  • How do you factor x^3 + 8 using the sum of cubes rule?
    It factors as (x + 2)(x^2 - 2x + 4).
  • What does the SOAP acronym stand for in factoring cubes?
    SOAP stands for Same, Opposite, Always Positive, describing the signs in the binomial and trinomial factors.
  • How do you factor 27y^3 - 1 using the difference of cubes rule?
    It factors as (3y - 1)(9y^2 + 3y + 1).