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Factoring Trinomials of the Form x² + bx + c quiz

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  • What is the general form of a trinomial that can be factored using the method discussed in the lesson?
    The general form is x² + bx + c, where the coefficient of x² is 1.
  • When factoring x² + bx + c, what do the two numbers you are looking for need to do?
    They must multiply to c and add to b.
  • What does the FOIL method stand for when multiplying two binomials?
    FOIL stands for First, Outside, Inside, Last, referring to the terms you multiply together.
  • In the trinomial x² + 10x + 21, what are the two numbers that multiply to 21 and add to 10?
    The numbers are 3 and 7.
  • How can you check if your factoring of a trinomial is correct?
    Multiply the two binomials back together to see if you get the original trinomial.
  • What is the factored form of x² + 10x + 21?
    It is (x + 3)(x + 7).
  • Why is it helpful to list all factor pairs of c when factoring trinomials?
    Listing factor pairs helps you systematically find which pair adds to b.
  • What is the first step when factoring x² + 3x - 28?
    Identify the values of b (3) and c (-28).
  • Which factor pair of -28 adds up to 3?
    The pair is -4 and 7.
  • What is the factored form of x² + 3x - 28?
    It is (x - 4)(x + 7).
  • For x² - 11x + 30, which factor pair of 30 adds to -11?
    The pair is -5 and -6.
  • What is the factored form of x² - 11x + 30?
    It is (x - 5)(x - 6).
  • Why must the coefficient of x² be 1 to use this factoring method?
    Because the method relies on the pattern that arises when the leading coefficient is 1; otherwise, the process is different.
  • What does the constant term c in the trinomial represent when factoring?
    It represents the product of the two constants in the binomials.
  • What does the coefficient b in the trinomial represent when factoring?
    It represents the sum of the two constants in the binomials.