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8x^2+16x-24

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To simplify or factor the expression \(8x^2 + 16x - 24\), we can start by factoring out the greatest common factor (GCF) of the terms.

  1. Identify the GCF: The coefficients 8, 16, and -24 have a GCF of 8.

  2. Factor out the GCF:

\[ 8(x^2 + 2x - 3) \]

  1. Factor the quadratic expression: Now, we need to factor the quadratic \(x^2 + 2x - 3\). We are looking for two numbers that multiply to -3 (the constant term) and add to 2 (the coefficient of the linear term).

    The numbers 3 and -1 work because \(3 \times (-1) = -3\) and \(3 + (-1) = 2\).

    Therefore, we can factor \(x^2 + 2x - 3\) as:

\[ (x + 3)(x - 1) \]

  1. Combine everything: Putting it all together, the factored form of the original expression is:

\[ 8(x + 3)(x - 1) \]

So, the complete factorization of \(8x^2 + 16x - 24\) is:

\[ 8(x + 3)(x - 1) \]