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Factor \(\displaystyle - 56 x^{3} - 48 x^{2} - 7 x - 6\).

Factoring out the GCF \(\displaystyle -1\) from each term gives \(\displaystyle -(56 x^{3} + 48 x^{2} + 7 x + 6)\). Grouping the first two terms and factoring out their GCF, \(\displaystyle 8 x^{2}\), gives \(\displaystyle 8 x^{2}(7 x + 6)\). Grouping the last two terms and factoring out their GCF, \(\displaystyle 1\), gives \(\displaystyle 1(7 x + 6)\). The polynomial now has a common binomial factor of \(\displaystyle 7 x + 6\). This gives \(\displaystyle -1[8 x^{2} \left(7 x + 6\right) +1 \cdot \left(7 x + 6\right)] = -\left(7 x + 6\right) \left(8 x^{2} + 1\right)\).

Download \(\LaTeX\) 

\begin{question}Factor $- 56 x^{3} - 48 x^{2} - 7 x - 6$. 
    \soln{9cm}{Factoring out the GCF $-1$ from each term gives $-(56 x^{3} + 48 x^{2} + 7 x + 6)$. Grouping the first two terms and factoring out their GCF, $8 x^{2}$, gives $8 x^{2}(7 x + 6)$. Grouping the last two terms and factoring out their GCF, $1$, gives $1(7 x + 6)$. The polynomial now has a common binomial factor of $7 x + 6$. This gives $-1[8 x^{2} \left(7 x + 6\right) +1 \cdot \left(7 x + 6\right)] = -\left(7 x + 6\right) \left(8 x^{2} + 1\right)$. }

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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HTML for Canvas 
<p> <p>Factor  <img class="equation_image" title=" \displaystyle - 56 x^{3} - 48 x^{2} - 7 x - 6 " src="/equation_images/%20%5Cdisplaystyle%20-%2056%20x%5E%7B3%7D%20-%2048%20x%5E%7B2%7D%20-%207%20x%20-%206%20" alt="LaTeX:  \displaystyle - 56 x^{3} - 48 x^{2} - 7 x - 6 " data-equation-content=" \displaystyle - 56 x^{3} - 48 x^{2} - 7 x - 6 " /> . </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 -(56 x^{3} + 48 x^{2} + 7 x + 6) " src="/equation_images/%20%5Cdisplaystyle%20-%2856%20x%5E%7B3%7D%20%2B%2048%20x%5E%7B2%7D%20%2B%207%20x%20%2B%206%29%20" alt="LaTeX:  \displaystyle -(56 x^{3} + 48 x^{2} + 7 x + 6) " data-equation-content=" \displaystyle -(56 x^{3} + 48 x^{2} + 7 x + 6) " /> . Grouping the first two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle 8 x^{2} " src="/equation_images/%20%5Cdisplaystyle%208%20x%5E%7B2%7D%20" alt="LaTeX:  \displaystyle 8 x^{2} " data-equation-content=" \displaystyle 8 x^{2} " /> , gives  <img class="equation_image" title=" \displaystyle 8 x^{2}(7 x + 6) " src="/equation_images/%20%5Cdisplaystyle%208%20x%5E%7B2%7D%287%20x%20%2B%206%29%20" alt="LaTeX:  \displaystyle 8 x^{2}(7 x + 6) " data-equation-content=" \displaystyle 8 x^{2}(7 x + 6) " /> . Grouping the last two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle 1 " src="/equation_images/%20%5Cdisplaystyle%201%20" alt="LaTeX:  \displaystyle 1 " data-equation-content=" \displaystyle 1 " /> , gives  <img class="equation_image" title=" \displaystyle 1(7 x + 6) " src="/equation_images/%20%5Cdisplaystyle%201%287%20x%20%2B%206%29%20" alt="LaTeX:  \displaystyle 1(7 x + 6) " data-equation-content=" \displaystyle 1(7 x + 6) " /> . The polynomial now has a common binomial factor of  <img class="equation_image" title=" \displaystyle 7 x + 6 " src="/equation_images/%20%5Cdisplaystyle%207%20x%20%2B%206%20" alt="LaTeX:  \displaystyle 7 x + 6 " data-equation-content=" \displaystyle 7 x + 6 " /> . This gives  <img class="equation_image" title=" \displaystyle -1[8 x^{2} \left(7 x + 6\right) +1 \cdot \left(7 x + 6\right)] = -\left(7 x + 6\right) \left(8 x^{2} + 1\right) " src="/equation_images/%20%5Cdisplaystyle%20-1%5B8%20x%5E%7B2%7D%20%5Cleft%287%20x%20%2B%206%5Cright%29%20%2B1%20%5Ccdot%20%5Cleft%287%20x%20%2B%206%5Cright%29%5D%20%3D%20-%5Cleft%287%20x%20%2B%206%5Cright%29%20%5Cleft%288%20x%5E%7B2%7D%20%2B%201%5Cright%29%20" alt="LaTeX:  \displaystyle -1[8 x^{2} \left(7 x + 6\right) +1 \cdot \left(7 x + 6\right)] = -\left(7 x + 6\right) \left(8 x^{2} + 1\right) " data-equation-content=" \displaystyle -1[8 x^{2} \left(7 x + 6\right) +1 \cdot \left(7 x + 6\right)] = -\left(7 x + 6\right) \left(8 x^{2} + 1\right) " /> . </p> </p>