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Factoring Trinomials in Beginning Algebra

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  • What is the general form of a trinomial to be factored?
    A trinomial in the form \(x^2 + bx + c\).
  • What does factoring a trinomial reverse?
    Factoring reverses the distributive property or FOIL method used to multiply binomials.
  • What is the FOIL method?
    FOIL stands for First, Outside, Inside, Last, the steps to multiply two binomials.
  • What is the product of two binomials (x + p)(x + q)?
    The product is \(x^2 + (p+q)x + pq\).
  • What two numbers must you find to factor \(x^2 + bx + c\)?
    Two numbers that multiply to c and add to b.
  • How do the two numbers found relate to the binomials in factoring?
    They become the constants in the binomials: (x + p)(x + q).
  • Factor the trinomial \(x^2 + 10x + 21\).
    Find two numbers that multiply to 21 and add to 10: 3 and 7. The factorization is (x + 3)(x + 7).
  • Why is recognizing the pattern \(x^2 + (p+q)x + pq\) important?
    It helps identify the correct numbers to factor the trinomial into binomials.
  • What is the first step in factoring a trinomial \(x^2 + bx + c\)?
    Find two numbers that multiply to c.
  • What is the second step in factoring a trinomial \(x^2 + bx + c\)?
    Check that those two numbers add to b.

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