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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 like 9t^2 and 54t?
    Write each term in factored form, including variables, and multiply all the common factors.
  • What is the GCF of 9t^2 and 54t?
    The GCF is 9t.
  • What is the first step in factoring a polynomial using the GCF?
    Identify the greatest common factor of 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.
  • How can you check your work after factoring out the GCF?
    Redistribute the GCF back into the factored expression to see if you get the original polynomial.
  • What is the GCF of 12a^2, 30a^3, and 42a^5?
    The GCF is 6a^2.
  • What is factoring by grouping and when is it used?
    Factoring by grouping is used for polynomials with four terms by grouping them into pairs and factoring out the GCF from each pair.
  • In the polynomial x^3 + 2x^2 + 3x + 6, what is the result after factoring by grouping?
    The factored form is (x^2 + 3)(x + 2).
  • What should you do if factoring by grouping does not immediately produce a common binomial?
    Rearrange the terms to pair up those with a common factor.
  • How do you check your answer after factoring by grouping?
    Multiply the factors back together using FOIL to ensure you get the original polynomial.
  • What is the GCF of 6x, 12x^3, and 24x^4?
    The GCF is 6x.
  • 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.