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Questions: Algebra BusinessCalculus
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Solve \(\displaystyle 3 x^{2} - 18 x - 48=0\)
Since the GCF is \(\displaystyle 3\) we need we factor out the GCF to get \(\displaystyle 3(x^{2} - 6 x - 16)\). This is now a pq method factoring. The factors of \(\displaystyle -16\) that add up to \(\displaystyle -6\) are \(\displaystyle 2\) and \(\displaystyle -8\). This gives \(\displaystyle 3(x + 2)(x - 8)=0\). The solutions are \(\displaystyle x = -2\) and \(\displaystyle x = 8\)
\begin{question}Solve $3 x^{2} - 18 x - 48=0$
\soln{9cm}{Since the GCF is $3$ we need we factor out the GCF to get $3(x^{2} - 6 x - 16)$. This is now a pq method factoring. The factors of $-16$ that add up to $-6$ are $2$ and $-8$. This gives $3(x + 2)(x - 8)=0$. The solutions are $x = -2$ and $x = 8$}
\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 3 x^{2} - 18 x - 48=0 " src="/equation_images/%20%5Cdisplaystyle%203%20x%5E%7B2%7D%20-%2018%20x%20-%2048%3D0%20" alt="LaTeX: \displaystyle 3 x^{2} - 18 x - 48=0 " data-equation-content=" \displaystyle 3 x^{2} - 18 x - 48=0 " /> </p> </p><p> <p>Since the GCF is <img class="equation_image" title=" \displaystyle 3 " src="/equation_images/%20%5Cdisplaystyle%203%20" alt="LaTeX: \displaystyle 3 " data-equation-content=" \displaystyle 3 " /> we need we factor out the GCF to get <img class="equation_image" title=" \displaystyle 3(x^{2} - 6 x - 16) " src="/equation_images/%20%5Cdisplaystyle%203%28x%5E%7B2%7D%20-%206%20x%20-%2016%29%20" alt="LaTeX: \displaystyle 3(x^{2} - 6 x - 16) " data-equation-content=" \displaystyle 3(x^{2} - 6 x - 16) " /> . This is now a pq method factoring. The factors of <img class="equation_image" title=" \displaystyle -16 " src="/equation_images/%20%5Cdisplaystyle%20-16%20" alt="LaTeX: \displaystyle -16 " data-equation-content=" \displaystyle -16 " /> 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 2 " src="/equation_images/%20%5Cdisplaystyle%202%20" alt="LaTeX: \displaystyle 2 " data-equation-content=" \displaystyle 2 " /> and <img class="equation_image" title=" \displaystyle -8 " src="/equation_images/%20%5Cdisplaystyle%20-8%20" alt="LaTeX: \displaystyle -8 " data-equation-content=" \displaystyle -8 " /> . This gives <img class="equation_image" title=" \displaystyle 3(x + 2)(x - 8)=0 " src="/equation_images/%20%5Cdisplaystyle%203%28x%20%2B%202%29%28x%20-%208%29%3D0%20" alt="LaTeX: \displaystyle 3(x + 2)(x - 8)=0 " data-equation-content=" \displaystyle 3(x + 2)(x - 8)=0 " /> . The solutions are <img class="equation_image" title=" \displaystyle x = -2 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-2%20" alt="LaTeX: \displaystyle x = -2 " data-equation-content=" \displaystyle x = -2 " /> and <img class="equation_image" title=" \displaystyle x = 8 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%208%20" alt="LaTeX: \displaystyle x = 8 " data-equation-content=" \displaystyle x = 8 " /> </p> </p>