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Factoring by Greatest Common Factor & Grouping quiz

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  • What does it mean to factor a number or term?
    To factor means to rewrite a number or term as a product of two or more numbers or terms.
  • How do you find the greatest common factor (GCF) of two numbers?
    Write each number in its prime factorization and multiply all their common prime factors together.
  • What is the GCF of 9 and 54?
    The GCF is 9, since both numbers share two factors of 3.
  • How do you find the GCF of terms like 9t^2 and 54t?
    Write each term in factored form, including variables, and multiply all common prime factors and variables.
  • What is the GCF of 9t^2 and 54t?
    The GCF is 9t, since both terms share two factors of 3 and one t.
  • What is the GCF of 12a^2, 30a^3, and 42a^5?
    The GCF is 6a^2, since all terms share factors of 2, 3, and at least two a's.
  • How can you check if a factor is the GCF of a set of terms?
    The GCF is the largest factor that evenly divides out of every term.
  • What is the first step in factoring a polynomial by GCF?
    Identify the greatest common factor by writing out the prime factorization for each term.
  • How do you factor out the GCF from a polynomial?
    Rewrite each term as a product with the GCF, then factor the GCF out of the polynomial.
  • What is the GCF of 6x, 12x^3, and -24x^4?
    The GCF is 6x, since all terms share factors of 2, 3, and x.
  • What is the result of factoring 6x + 12x^3 - 24x^4 by GCF?
    The result is 6x(1 + 2x^2 - 4x^3).
  • When should you try to factor out the GCF first?
    Always try to factor out the GCF first to help simplify the polynomial before using other methods.
  • What is factoring by grouping used for?
    Factoring by grouping is used when a polynomial has four terms.
  • What is the first step in factoring by grouping?
    Group the terms into two pairs and factor the GCF out of each pair.
  • How do you check your answer after factoring by grouping?
    Multiply the factors back together using FOIL to confirm you get the original polynomial.