Tony is trying to find the solutions to the quadratic equation 3×2 + 24x – 15 = 0 by factoring and has come to you for help. Explain w

Question

Tony is trying to find the solutions to the quadratic equation 3×2 + 24x – 15 = 0 by factoring and
has come to you for help. Explain why Tony would need to use a method other than factoring to find
the solutions to this equation.
DO NOT SOLVE and be specific in your explanation.
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Mít Mít 4 years 2021-07-29T06:05:38+00:00 1 Answers 12 views 0

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  1. minhkhoi
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    2021-07-29T06:06:54+00:00
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    Answer:

    You would either need to complete the square, use the quadratic equation, or another method because when reduced by the common factor, the constant term c is prime which means that it is only divisible by one and itself. Because the possible rational factors determined by c do not add up to the b term, it cannot be factored.

    Explanation:

    3x² + 24x – 15 = 0

    3(x² + 8x – 5) = 0

    [find the greatest common factor between each term and move the coefficient outside of the expression; in this case it’s 3 since 3 fits into numbers 3, 24, and -15 so that it cannot be reduced further]

    Then you can either use the box or pq method (since a is 1) to find working factors.

    x² + bx + c → (x + p)(x + q).

    p + q = b.

    pq = c.

    In this case with 3(x² + 8x – 5), b is 8 and c is -5.

    This means we need two numbers that add up to 8 and multiply to -5.

    Since -5 is prime, our only options are ±1 for p and ∓5 for q. This is because these are the only factors which multiply to -5.

    1 + -5 = -4 ≠ 8

    -1 + 5 = 4 ≠ 8.

    Since we cannot find rational solutions, this cannot be factored, and so we must use another method.

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