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Factor \(\displaystyle - 12 x^{3} - 30 x^{2} - 14 x - 35\).

Factoring out the GCF \(\displaystyle -1\) from each term gives \(\displaystyle -(12 x^{3} + 30 x^{2} + 14 x + 35)\). Grouping the first two terms and factoring out their GCF, \(\displaystyle 6 x^{2}\), gives \(\displaystyle 6 x^{2}(2 x + 5)\). Grouping the last two terms and factoring out their GCF, \(\displaystyle 7\), gives \(\displaystyle 7(2 x + 5)\). The polynomial now has a common binomial factor of \(\displaystyle 2 x + 5\). This gives \(\displaystyle -1[6 x^{2} \left(2 x + 5\right) +7 \cdot \left(2 x + 5\right)] = -\left(2 x + 5\right) \left(6 x^{2} + 7\right)\).

Download \(\LaTeX\) 

\begin{question}Factor $- 12 x^{3} - 30 x^{2} - 14 x - 35$. 
    \soln{9cm}{Factoring out the GCF $-1$ from each term gives $-(12 x^{3} + 30 x^{2} + 14 x + 35)$. Grouping the first two terms and factoring out their GCF, $6 x^{2}$, gives $6 x^{2}(2 x + 5)$. Grouping the last two terms and factoring out their GCF, $7$, gives $7(2 x + 5)$. The polynomial now has a common binomial factor of $2 x + 5$. This gives $-1[6 x^{2} \left(2 x + 5\right) +7 \cdot \left(2 x + 5\right)] = -\left(2 x + 5\right) \left(6 x^{2} + 7\right)$. }

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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HTML for Canvas 
<p> <p>Factor  <img class="equation_image" title=" \displaystyle - 12 x^{3} - 30 x^{2} - 14 x - 35 " src="/equation_images/%20%5Cdisplaystyle%20-%2012%20x%5E%7B3%7D%20-%2030%20x%5E%7B2%7D%20-%2014%20x%20-%2035%20" alt="LaTeX:  \displaystyle - 12 x^{3} - 30 x^{2} - 14 x - 35 " data-equation-content=" \displaystyle - 12 x^{3} - 30 x^{2} - 14 x - 35 " /> . </p> </p>
HTML for Canvas
<p> <p>Factoring out the GCF  <img class="equation_image" title=" \displaystyle -1 " src="/equation_images/%20%5Cdisplaystyle%20-1%20" alt="LaTeX:  \displaystyle -1 " data-equation-content=" \displaystyle -1 " />  from each term gives  <img class="equation_image" title=" \displaystyle -(12 x^{3} + 30 x^{2} + 14 x + 35) " src="/equation_images/%20%5Cdisplaystyle%20-%2812%20x%5E%7B3%7D%20%2B%2030%20x%5E%7B2%7D%20%2B%2014%20x%20%2B%2035%29%20" alt="LaTeX:  \displaystyle -(12 x^{3} + 30 x^{2} + 14 x + 35) " data-equation-content=" \displaystyle -(12 x^{3} + 30 x^{2} + 14 x + 35) " /> . Grouping the first two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle 6 x^{2} " src="/equation_images/%20%5Cdisplaystyle%206%20x%5E%7B2%7D%20" alt="LaTeX:  \displaystyle 6 x^{2} " data-equation-content=" \displaystyle 6 x^{2} " /> , gives  <img class="equation_image" title=" \displaystyle 6 x^{2}(2 x + 5) " src="/equation_images/%20%5Cdisplaystyle%206%20x%5E%7B2%7D%282%20x%20%2B%205%29%20" alt="LaTeX:  \displaystyle 6 x^{2}(2 x + 5) " data-equation-content=" \displaystyle 6 x^{2}(2 x + 5) " /> . Grouping the last two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle 7 " src="/equation_images/%20%5Cdisplaystyle%207%20" alt="LaTeX:  \displaystyle 7 " data-equation-content=" \displaystyle 7 " /> , gives  <img class="equation_image" title=" \displaystyle 7(2 x + 5) " src="/equation_images/%20%5Cdisplaystyle%207%282%20x%20%2B%205%29%20" alt="LaTeX:  \displaystyle 7(2 x + 5) " data-equation-content=" \displaystyle 7(2 x + 5) " /> . The polynomial now has a common binomial factor of  <img class="equation_image" title=" \displaystyle 2 x + 5 " src="/equation_images/%20%5Cdisplaystyle%202%20x%20%2B%205%20" alt="LaTeX:  \displaystyle 2 x + 5 " data-equation-content=" \displaystyle 2 x + 5 " /> . This gives  <img class="equation_image" title=" \displaystyle -1[6 x^{2} \left(2 x + 5\right) +7 \cdot \left(2 x + 5\right)] = -\left(2 x + 5\right) \left(6 x^{2} + 7\right) " src="/equation_images/%20%5Cdisplaystyle%20-1%5B6%20x%5E%7B2%7D%20%5Cleft%282%20x%20%2B%205%5Cright%29%20%2B7%20%5Ccdot%20%5Cleft%282%20x%20%2B%205%5Cright%29%5D%20%3D%20-%5Cleft%282%20x%20%2B%205%5Cright%29%20%5Cleft%286%20x%5E%7B2%7D%20%2B%207%5Cright%29%20" alt="LaTeX:  \displaystyle -1[6 x^{2} \left(2 x + 5\right) +7 \cdot \left(2 x + 5\right)] = -\left(2 x + 5\right) \left(6 x^{2} + 7\right) " data-equation-content=" \displaystyle -1[6 x^{2} \left(2 x + 5\right) +7 \cdot \left(2 x + 5\right)] = -\left(2 x + 5\right) \left(6 x^{2} + 7\right) " /> . </p> </p>