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8x^2+16x-24
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Answered by
GPT-4o mini
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**:
\[
8(x^2 + 2x - 3)
\]
3. **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:
\[
(x + 3)(x - 1)
\]
4. **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:
\[
8(x + 3)(x - 1)
\]
1. **Identify the GCF**: The coefficients 8, 16, and -24 have a GCF of 8.
2. **Factor out the GCF**:
\[
8(x^2 + 2x - 3)
\]
3. **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:
\[
(x + 3)(x - 1)
\]
4. **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:
\[
8(x + 3)(x - 1)
\]
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