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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 the 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 with variables, like 9t² and 54t?
    Write each term in factored form, including variables, and multiply all the common factors, including the lowest power of each variable.
  • What is the GCF of 12a², 30a³, and 42a⁵?
    The GCF is 6a², since each term has a factor of 2, 3, and at least a².
  • What is the first step in factoring a polynomial using the GCF?
    Identify the greatest common factor among all the terms in the polynomial.
  • After finding the GCF, what is the next step in factoring a polynomial?
    Rewrite each term as a product with the GCF, then factor the GCF out of the polynomial.
  • How can you check your work after factoring out the GCF?
    Redistribute (multiply) the GCF back into the factored polynomial to see if you get the original expression.
  • What is the GCF of 6x, 12x³, and 24x⁴?
    The GCF is 6x, since each term contains a factor of 6 and at least one x.
  • What is factoring by grouping and when is it used?
    Factoring by grouping is used for polynomials with four terms, grouping them into two pairs and factoring the GCF from each pair.
  • What should you do if factoring by grouping does not immediately produce a common binomial?
    Rearrange the terms to pair up terms that have a common factor, then try factoring by grouping again.
  • In the polynomial x³ + 2x² + 3x + 6, what is the result after factoring by grouping?
    The factored form is (x + 2)(x² + 3).
  • How do you check your answer after factoring by grouping?
    Multiply the factors back together using the FOIL method to ensure you get the original polynomial.
  • Why is it important to factor out the GCF before using other factoring methods?
    Factoring out the GCF simplifies the polynomial, making further factoring easier and more efficient.
  • What is the definition of the GCF for a list of terms?
    The GCF is the largest factor that evenly divides out of every term in the list.