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Questions: Algebra BusinessCalculus
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Solve \(\displaystyle - 3 x^{2} - 9 x + 12=0\)
Since the GCF is \(\displaystyle -3\) we need we factor out the GCF to get \(\displaystyle -3(x^{2} + 3 x - 4)\). This is now a pq method factoring. The factors of \(\displaystyle -4\) that add up to \(\displaystyle 3\) are \(\displaystyle -1\) and \(\displaystyle 4\). This gives \(\displaystyle -3(x - 1)(x + 4)=0\). The solutions are \(\displaystyle x = 1\) and \(\displaystyle x = -4\)
\begin{question}Solve $- 3 x^{2} - 9 x + 12=0$
\soln{9cm}{Since the GCF is $-3$ we need we factor out the GCF to get $-3(x^{2} + 3 x - 4)$. This is now a pq method factoring. The factors of $-4$ that add up to $3$ are $-1$ and $4$. This gives $-3(x - 1)(x + 4)=0$. The solutions are $x = 1$ and $x = -4$}
\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 + 12=0 " src="/equation_images/%20%5Cdisplaystyle%20-%203%20x%5E%7B2%7D%20-%209%20x%20%2B%2012%3D0%20" alt="LaTeX: \displaystyle - 3 x^{2} - 9 x + 12=0 " data-equation-content=" \displaystyle - 3 x^{2} - 9 x + 12=0 " /> </p> </p><p> <p>Since the GCF is <img class="equation_image" title=" \displaystyle -3 " src="/equation_images/%20%5Cdisplaystyle%20-3%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 - 4) " src="/equation_images/%20%5Cdisplaystyle%20-3%28x%5E%7B2%7D%20%2B%203%20x%20-%204%29%20" alt="LaTeX: \displaystyle -3(x^{2} + 3 x - 4) " data-equation-content=" \displaystyle -3(x^{2} + 3 x - 4) " /> . This is now a pq method factoring. The factors of <img class="equation_image" title=" \displaystyle -4 " src="/equation_images/%20%5Cdisplaystyle%20-4%20" alt="LaTeX: \displaystyle -4 " data-equation-content=" \displaystyle -4 " /> that add up to <img class="equation_image" title=" \displaystyle 3 " src="/equation_images/%20%5Cdisplaystyle%203%20" alt="LaTeX: \displaystyle 3 " data-equation-content=" \displaystyle 3 " /> are <img class="equation_image" title=" \displaystyle -1 " src="/equation_images/%20%5Cdisplaystyle%20-1%20" alt="LaTeX: \displaystyle -1 " data-equation-content=" \displaystyle -1 " /> and <img class="equation_image" title=" \displaystyle 4 " src="/equation_images/%20%5Cdisplaystyle%204%20" alt="LaTeX: \displaystyle 4 " data-equation-content=" \displaystyle 4 " /> . This gives <img class="equation_image" title=" \displaystyle -3(x - 1)(x + 4)=0 " src="/equation_images/%20%5Cdisplaystyle%20-3%28x%20-%201%29%28x%20%2B%204%29%3D0%20" alt="LaTeX: \displaystyle -3(x - 1)(x + 4)=0 " data-equation-content=" \displaystyle -3(x - 1)(x + 4)=0 " /> . The solutions are <img class="equation_image" title=" \displaystyle x = 1 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%201%20" alt="LaTeX: \displaystyle x = 1 " data-equation-content=" \displaystyle x = 1 " /> and <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 " /> </p> </p>