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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.
  • What does the FOIL method help you do when factoring trinomials?
    The FOIL method helps you multiply two binomials to get a trinomial, showing how the constants relate to the terms in the trinomial.
  • What must the two constants in the binomials multiply to when factoring x² + bx + c?
    They must multiply to the constant term c in the trinomial.
  • What must the two constants in the binomials add up to when factoring x² + bx + c?
    They must add up to the coefficient b of the x term in the trinomial.
  • How do you factor x² + 10x + 21 using the method taught?
    Find two numbers that multiply to 21 and add to 10; these are 3 and 7, so the factors are (x + 3)(x + 7).
  • What is the first step when factoring a trinomial like x² + 3x - 28?
    Identify the values of b and c, which are 3 and -28 respectively.
  • Why is a t-chart useful when factoring trinomials with larger or negative constants?
    A t-chart helps organize all possible factor pairs of c to easily check which pair adds to b.
  • What are the factor pairs of -28 that add up to 3?
    The pair is -4 and 7, since -4 + 7 = 3 and -4 × 7 = -28.
  • How would you write the factored form of x² + 3x - 28?
    The factored form is (x - 4)(x + 7).
  • What are the factor pairs of 30 that add up to -11?
    The pair is -5 and -6, since -5 + -6 = -11 and -5 × -6 = 30.
  • How would you write the factored form of x² - 11x + 30?
    The factored form is (x - 5)(x - 6).
  • What should you do to check your factoring work?
    Multiply the binomials back together to ensure you get the original trinomial.
  • When can you use this factoring technique for trinomials?
    You can use it only when the coefficient of x² is 1.
  • What is the relationship between the middle term b and the constants in the binomials?
    The middle term b is the sum of the two constants from the binomials.
  • What is the relationship between the constant term c and the constants in the binomials?
    The constant term c is the product of the two constants from the binomials.