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Factor \(\displaystyle - 48 x^{3} - 18 x^{2} - 80 x - 30\).

Factoring out the GCF \(\displaystyle -2\) from each term gives \(\displaystyle -2(24 x^{3} + 9 x^{2} + 40 x + 15)\). Grouping the first two terms and factoring out their GCF, \(\displaystyle 3 x^{2}\), gives \(\displaystyle 3 x^{2}(8 x + 3)\). Grouping the last two terms and factoring out their GCF, \(\displaystyle 5\), gives \(\displaystyle 5(8 x + 3)\). The polynomial now has a common binomial factor of \(\displaystyle 8 x + 3\). This gives \(\displaystyle -2[3 x^{2} \left(8 x + 3\right) +5 \cdot \left(8 x + 3\right)] = -2\left(8 x + 3\right) \left(3 x^{2} + 5\right)\).

Download \(\LaTeX\) 

\begin{question}Factor $- 48 x^{3} - 18 x^{2} - 80 x - 30$. 
    \soln{9cm}{Factoring out the GCF $-2$ from each term gives $-2(24 x^{3} + 9 x^{2} + 40 x + 15)$. Grouping the first two terms and factoring out their GCF, $3 x^{2}$, gives $3 x^{2}(8 x + 3)$. Grouping the last two terms and factoring out their GCF, $5$, gives $5(8 x + 3)$. The polynomial now has a common binomial factor of $8 x + 3$. This gives $-2[3 x^{2} \left(8 x + 3\right) +5 \cdot \left(8 x + 3\right)] = -2\left(8 x + 3\right) \left(3 x^{2} + 5\right)$. }

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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HTML for Canvas 
<p> <p>Factor  <img class="equation_image" title=" \displaystyle - 48 x^{3} - 18 x^{2} - 80 x - 30 " src="/equation_images/%20%5Cdisplaystyle%20-%2048%20x%5E%7B3%7D%20-%2018%20x%5E%7B2%7D%20-%2080%20x%20-%2030%20" alt="LaTeX:  \displaystyle - 48 x^{3} - 18 x^{2} - 80 x - 30 " data-equation-content=" \displaystyle - 48 x^{3} - 18 x^{2} - 80 x - 30 " /> . </p> </p>
HTML for Canvas
<p> <p>Factoring out the GCF  <img class="equation_image" title=" \displaystyle -2 " src="/equation_images/%20%5Cdisplaystyle%20-2%20" alt="LaTeX:  \displaystyle -2 " data-equation-content=" \displaystyle -2 " />  from each term gives  <img class="equation_image" title=" \displaystyle -2(24 x^{3} + 9 x^{2} + 40 x + 15) " src="/equation_images/%20%5Cdisplaystyle%20-2%2824%20x%5E%7B3%7D%20%2B%209%20x%5E%7B2%7D%20%2B%2040%20x%20%2B%2015%29%20" alt="LaTeX:  \displaystyle -2(24 x^{3} + 9 x^{2} + 40 x + 15) " data-equation-content=" \displaystyle -2(24 x^{3} + 9 x^{2} + 40 x + 15) " /> . Grouping the first two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle 3 x^{2} " src="/equation_images/%20%5Cdisplaystyle%203%20x%5E%7B2%7D%20" alt="LaTeX:  \displaystyle 3 x^{2} " data-equation-content=" \displaystyle 3 x^{2} " /> , gives  <img class="equation_image" title=" \displaystyle 3 x^{2}(8 x + 3) " src="/equation_images/%20%5Cdisplaystyle%203%20x%5E%7B2%7D%288%20x%20%2B%203%29%20" alt="LaTeX:  \displaystyle 3 x^{2}(8 x + 3) " data-equation-content=" \displaystyle 3 x^{2}(8 x + 3) " /> . Grouping the last two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle 5 " src="/equation_images/%20%5Cdisplaystyle%205%20" alt="LaTeX:  \displaystyle 5 " data-equation-content=" \displaystyle 5 " /> , gives  <img class="equation_image" title=" \displaystyle 5(8 x + 3) " src="/equation_images/%20%5Cdisplaystyle%205%288%20x%20%2B%203%29%20" alt="LaTeX:  \displaystyle 5(8 x + 3) " data-equation-content=" \displaystyle 5(8 x + 3) " /> . The polynomial now has a common binomial factor of  <img class="equation_image" title=" \displaystyle 8 x + 3 " src="/equation_images/%20%5Cdisplaystyle%208%20x%20%2B%203%20" alt="LaTeX:  \displaystyle 8 x + 3 " data-equation-content=" \displaystyle 8 x + 3 " /> . This gives  <img class="equation_image" title=" \displaystyle -2[3 x^{2} \left(8 x + 3\right) +5 \cdot \left(8 x + 3\right)] = -2\left(8 x + 3\right) \left(3 x^{2} + 5\right) " src="/equation_images/%20%5Cdisplaystyle%20-2%5B3%20x%5E%7B2%7D%20%5Cleft%288%20x%20%2B%203%5Cright%29%20%2B5%20%5Ccdot%20%5Cleft%288%20x%20%2B%203%5Cright%29%5D%20%3D%20-2%5Cleft%288%20x%20%2B%203%5Cright%29%20%5Cleft%283%20x%5E%7B2%7D%20%2B%205%5Cright%29%20" alt="LaTeX:  \displaystyle -2[3 x^{2} \left(8 x + 3\right) +5 \cdot \left(8 x + 3\right)] = -2\left(8 x + 3\right) \left(3 x^{2} + 5\right) " data-equation-content=" \displaystyle -2[3 x^{2} \left(8 x + 3\right) +5 \cdot \left(8 x + 3\right)] = -2\left(8 x + 3\right) \left(3 x^{2} + 5\right) " /> . </p> </p>