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Questions: Algebra BusinessCalculus
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Solve \(\displaystyle 3 x^{2} - 9 x - 84=0\)
Since the GCF is \(\displaystyle 3\) we need we factor out the GCF to get \(\displaystyle 3(x^{2} - 3 x - 28)\). This is now a pq method factoring. The factors of \(\displaystyle -28\) that add up to \(\displaystyle -3\) are \(\displaystyle 4\) and \(\displaystyle -7\). This gives \(\displaystyle 3(x + 4)(x - 7)=0\). The solutions are \(\displaystyle x = -4\) and \(\displaystyle x = 7\)
\begin{question}Solve $3 x^{2} - 9 x - 84=0$
\soln{9cm}{Since the GCF is $3$ we need we factor out the GCF to get $3(x^{2} - 3 x - 28)$. This is now a pq method factoring. The factors of $-28$ that add up to $-3$ are $4$ and $-7$. This gives $3(x + 4)(x - 7)=0$. The solutions are $x = -4$ and $x = 7$}
\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} - 9 x - 84=0 " src="/equation_images/%20%5Cdisplaystyle%203%20x%5E%7B2%7D%20-%209%20x%20-%2084%3D0%20" alt="LaTeX: \displaystyle 3 x^{2} - 9 x - 84=0 " data-equation-content=" \displaystyle 3 x^{2} - 9 x - 84=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} - 3 x - 28) " src="/equation_images/%20%5Cdisplaystyle%203%28x%5E%7B2%7D%20-%203%20x%20-%2028%29%20" alt="LaTeX: \displaystyle 3(x^{2} - 3 x - 28) " data-equation-content=" \displaystyle 3(x^{2} - 3 x - 28) " /> . This is now a pq method factoring. The factors of <img class="equation_image" title=" \displaystyle -28 " src="/equation_images/%20%5Cdisplaystyle%20-28%20" alt="LaTeX: \displaystyle -28 " data-equation-content=" \displaystyle -28 " /> that add up to <img class="equation_image" title=" \displaystyle -3 " src="/equation_images/%20%5Cdisplaystyle%20-3%20" alt="LaTeX: \displaystyle -3 " data-equation-content=" \displaystyle -3 " /> are <img class="equation_image" title=" \displaystyle 4 " src="/equation_images/%20%5Cdisplaystyle%204%20" alt="LaTeX: \displaystyle 4 " data-equation-content=" \displaystyle 4 " /> and <img class="equation_image" title=" \displaystyle -7 " src="/equation_images/%20%5Cdisplaystyle%20-7%20" alt="LaTeX: \displaystyle -7 " data-equation-content=" \displaystyle -7 " /> . This gives <img class="equation_image" title=" \displaystyle 3(x + 4)(x - 7)=0 " src="/equation_images/%20%5Cdisplaystyle%203%28x%20%2B%204%29%28x%20-%207%29%3D0%20" alt="LaTeX: \displaystyle 3(x + 4)(x - 7)=0 " data-equation-content=" \displaystyle 3(x + 4)(x - 7)=0 " /> . The solutions are <img class="equation_image" title=" \displaystyle x = -4 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-4%20" alt="LaTeX: \displaystyle x = -4 " data-equation-content=" \displaystyle x = -4 " /> and <img class="equation_image" title=" \displaystyle x = 7 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%207%20" alt="LaTeX: \displaystyle x = 7 " data-equation-content=" \displaystyle x = 7 " /> </p> </p>