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Factor \(\displaystyle - 56 x^{3} - 49 x^{2} + 48 x + 42\).

Factoring out the GCF \(\displaystyle -1\) from each term gives \(\displaystyle -(56 x^{3} + 49 x^{2} - 48 x - 42)\). Grouping the first two terms and factoring out their GCF, \(\displaystyle 7 x^{2}\), gives \(\displaystyle 7 x^{2}(8 x + 7)\). Grouping the last two terms and factoring out their GCF, \(\displaystyle -6\), gives \(\displaystyle -6(8 x + 7)\). The polynomial now has a common binomial factor of \(\displaystyle 8 x + 7\). This gives \(\displaystyle -1[7 x^{2} \left(8 x + 7\right) -6 \cdot \left(8 x + 7\right)] = -\left(8 x + 7\right) \left(7 x^{2} - 6\right)\).

Download \(\LaTeX\) 

\begin{question}Factor $- 56 x^{3} - 49 x^{2} + 48 x + 42$. 
    \soln{9cm}{Factoring out the GCF $-1$ from each term gives $-(56 x^{3} + 49 x^{2} - 48 x - 42)$. Grouping the first two terms and factoring out their GCF, $7 x^{2}$, gives $7 x^{2}(8 x + 7)$. Grouping the last two terms and factoring out their GCF, $-6$, gives $-6(8 x + 7)$. The polynomial now has a common binomial factor of $8 x + 7$. This gives $-1[7 x^{2} \left(8 x + 7\right) -6 \cdot \left(8 x + 7\right)] = -\left(8 x + 7\right) \left(7 x^{2} - 6\right)$. }

\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} - 49 x^{2} + 48 x + 42 " src="/equation_images/%20%5Cdisplaystyle%20-%2056%20x%5E%7B3%7D%20-%2049%20x%5E%7B2%7D%20%2B%2048%20x%20%2B%2042%20" alt="LaTeX:  \displaystyle - 56 x^{3} - 49 x^{2} + 48 x + 42 " data-equation-content=" \displaystyle - 56 x^{3} - 49 x^{2} + 48 x + 42 " /> . </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} + 49 x^{2} - 48 x - 42) " src="/equation_images/%20%5Cdisplaystyle%20-%2856%20x%5E%7B3%7D%20%2B%2049%20x%5E%7B2%7D%20-%2048%20x%20-%2042%29%20" alt="LaTeX:  \displaystyle -(56 x^{3} + 49 x^{2} - 48 x - 42) " data-equation-content=" \displaystyle -(56 x^{3} + 49 x^{2} - 48 x - 42) " /> . Grouping the first two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle 7 x^{2} " src="/equation_images/%20%5Cdisplaystyle%207%20x%5E%7B2%7D%20" alt="LaTeX:  \displaystyle 7 x^{2} " data-equation-content=" \displaystyle 7 x^{2} " /> , gives  <img class="equation_image" title=" \displaystyle 7 x^{2}(8 x + 7) " src="/equation_images/%20%5Cdisplaystyle%207%20x%5E%7B2%7D%288%20x%20%2B%207%29%20" alt="LaTeX:  \displaystyle 7 x^{2}(8 x + 7) " data-equation-content=" \displaystyle 7 x^{2}(8 x + 7) " /> . Grouping the last two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle -6 " src="/equation_images/%20%5Cdisplaystyle%20-6%20" alt="LaTeX:  \displaystyle -6 " data-equation-content=" \displaystyle -6 " /> , gives  <img class="equation_image" title=" \displaystyle -6(8 x + 7) " src="/equation_images/%20%5Cdisplaystyle%20-6%288%20x%20%2B%207%29%20" alt="LaTeX:  \displaystyle -6(8 x + 7) " data-equation-content=" \displaystyle -6(8 x + 7) " /> . The polynomial now has a common binomial factor of  <img class="equation_image" title=" \displaystyle 8 x + 7 " src="/equation_images/%20%5Cdisplaystyle%208%20x%20%2B%207%20" alt="LaTeX:  \displaystyle 8 x + 7 " data-equation-content=" \displaystyle 8 x + 7 " /> . This gives  <img class="equation_image" title=" \displaystyle -1[7 x^{2} \left(8 x + 7\right) -6 \cdot \left(8 x + 7\right)] = -\left(8 x + 7\right) \left(7 x^{2} - 6\right) " src="/equation_images/%20%5Cdisplaystyle%20-1%5B7%20x%5E%7B2%7D%20%5Cleft%288%20x%20%2B%207%5Cright%29%20-6%20%5Ccdot%20%5Cleft%288%20x%20%2B%207%5Cright%29%5D%20%3D%20-%5Cleft%288%20x%20%2B%207%5Cright%29%20%5Cleft%287%20x%5E%7B2%7D%20-%206%5Cright%29%20" alt="LaTeX:  \displaystyle -1[7 x^{2} \left(8 x + 7\right) -6 \cdot \left(8 x + 7\right)] = -\left(8 x + 7\right) \left(7 x^{2} - 6\right) " data-equation-content=" \displaystyle -1[7 x^{2} \left(8 x + 7\right) -6 \cdot \left(8 x + 7\right)] = -\left(8 x + 7\right) \left(7 x^{2} - 6\right) " /> . </p> </p>