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Questions: Algebra BusinessCalculus
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Solve \(\displaystyle 4 x^{2} - 24 x - 108=0\)
Since the GCF is \(\displaystyle 4\) we need we factor out the GCF to get \(\displaystyle 4(x^{2} - 6 x - 27)\). This is now a pq method factoring. The factors of \(\displaystyle -27\) that add up to \(\displaystyle -6\) are \(\displaystyle 3\) and \(\displaystyle -9\). This gives \(\displaystyle 4(x + 3)(x - 9)=0\). The solutions are \(\displaystyle x = -3\) and \(\displaystyle x = 9\)
\begin{question}Solve $4 x^{2} - 24 x - 108=0$
\soln{9cm}{Since the GCF is $4$ we need we factor out the GCF to get $4(x^{2} - 6 x - 27)$. This is now a pq method factoring. The factors of $-27$ that add up to $-6$ are $3$ and $-9$. This gives $4(x + 3)(x - 9)=0$. The solutions are $x = -3$ and $x = 9$}
\end{question}
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\begin{document}\begin{question}(10pts) The question goes here!
\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>Solve <img class="equation_image" title=" \displaystyle 4 x^{2} - 24 x - 108=0 " src="/equation_images/%20%5Cdisplaystyle%204%20x%5E%7B2%7D%20-%2024%20x%20-%20108%3D0%20" alt="LaTeX: \displaystyle 4 x^{2} - 24 x - 108=0 " data-equation-content=" \displaystyle 4 x^{2} - 24 x - 108=0 " /> </p> </p><p> <p>Since the GCF is <img class="equation_image" title=" \displaystyle 4 " src="/equation_images/%20%5Cdisplaystyle%204%20" alt="LaTeX: \displaystyle 4 " data-equation-content=" \displaystyle 4 " /> we need we factor out the GCF to get <img class="equation_image" title=" \displaystyle 4(x^{2} - 6 x - 27) " src="/equation_images/%20%5Cdisplaystyle%204%28x%5E%7B2%7D%20-%206%20x%20-%2027%29%20" alt="LaTeX: \displaystyle 4(x^{2} - 6 x - 27) " data-equation-content=" \displaystyle 4(x^{2} - 6 x - 27) " /> . This is now a pq method factoring. The factors of <img class="equation_image" title=" \displaystyle -27 " src="/equation_images/%20%5Cdisplaystyle%20-27%20" alt="LaTeX: \displaystyle -27 " data-equation-content=" \displaystyle -27 " /> that add up to <img class="equation_image" title=" \displaystyle -6 " src="/equation_images/%20%5Cdisplaystyle%20-6%20" alt="LaTeX: \displaystyle -6 " data-equation-content=" \displaystyle -6 " /> are <img class="equation_image" title=" \displaystyle 3 " src="/equation_images/%20%5Cdisplaystyle%203%20" alt="LaTeX: \displaystyle 3 " data-equation-content=" \displaystyle 3 " /> and <img class="equation_image" title=" \displaystyle -9 " src="/equation_images/%20%5Cdisplaystyle%20-9%20" alt="LaTeX: \displaystyle -9 " data-equation-content=" \displaystyle -9 " /> . This gives <img class="equation_image" title=" \displaystyle 4(x + 3)(x - 9)=0 " src="/equation_images/%20%5Cdisplaystyle%204%28x%20%2B%203%29%28x%20-%209%29%3D0%20" alt="LaTeX: \displaystyle 4(x + 3)(x - 9)=0 " data-equation-content=" \displaystyle 4(x + 3)(x - 9)=0 " /> . The solutions are <img class="equation_image" title=" \displaystyle x = -3 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-3%20" alt="LaTeX: \displaystyle x = -3 " data-equation-content=" \displaystyle x = -3 " /> and <img class="equation_image" title=" \displaystyle x = 9 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%209%20" alt="LaTeX: \displaystyle x = 9 " data-equation-content=" \displaystyle x = 9 " /> </p> </p>