Pregunta
al. Look for a GCF first. 11. \( 6 a^{2}+9 a-27 \)
Ask by Donnelly Vaughn. in the United States
Mar 12,2025
Solución de inteligencia artificial de Upstudy
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The greatest common factor of \(6a^{2}+9a-27\) is 3.
Solución
To find the greatest common factor (GCF) of the expression \(6a^{2}+9a-27\), we need to factorize the expression.
The expression can be factored as follows:
\[6a^{2}+9a-27 = 3(2a^{2}+3a-9)\]
Therefore, the greatest common factor of the expression \(6a^{2}+9a-27\) is 3.
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Simplifique esta solución Extra Insights
To begin solving \( 6a^2 + 9a - 27 \), let's factor out the greatest common factor (GCF). The GCF here is 3, which can be factored out to simplify the expression to \( 3(2a^2 + 3a - 9) \). Next, we can focus on factoring the quadratic \( 2a^2 + 3a - 9 \). To do this, look for two numbers that multiply to \( 2 \times (-9) = -18 \) and add to \( 3 \). The numbers \( 6 \) and \( -3 \) work perfectly! You can rewrite the middle term and factor by grouping. The fully factored form of your original expression is \( 3(2a - 3)(a + 3) \).
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