Algebra 1b

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Explain how to factor the following trinomials forms: x² + bx + c and ax² + bx + c. Is there more than one way to factor this? Show your answer using both words and mathematical notation.

  • Algebra 1b -

    Let's factor the trinomial x² + bx + c. We know that if b²-4c >= 0 then this trinomial has zeros and it can be factorized. It's zeros are

    x1 = [ -b + √(b²-4c) ] / 2

    and

    x2 = [ -b - √(b²-4c) ] / 2.

    So, we can factor it as

    x² + bx + c = (x-x1)(x-x2).

    In a case of trinomial ax² + bx + c we can factorize it as

    ax² + bx + c = a(x² + b/a·x + c/a),

    where the trinomial x² + b/a·x + c/a has the same form as x² + bx + c.

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