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Factor \(\displaystyle - 6 x^{3} - 42 x^{2} + 8 x + 56\).

Factoring out the GCF \(\displaystyle -2\) from each term gives \(\displaystyle -2(3 x^{3} + 21 x^{2} - 4 x - 28)\). Grouping the first two terms and factoring out their GCF, \(\displaystyle 3 x^{2}\), gives \(\displaystyle 3 x^{2}(x + 7)\). Grouping the last two terms and factoring out their GCF, \(\displaystyle -4\), gives \(\displaystyle -4(x + 7)\). The polynomial now has a common binomial factor of \(\displaystyle x + 7\). This gives \(\displaystyle -2[3 x^{2} \left(x + 7\right) -4 \cdot \left(x + 7\right)] = -2\left(x + 7\right) \left(3 x^{2} - 4\right)\).

Download \(\LaTeX\) 

\begin{question}Factor $- 6 x^{3} - 42 x^{2} + 8 x + 56$. 
    \soln{9cm}{Factoring out the GCF $-2$ from each term gives $-2(3 x^{3} + 21 x^{2} - 4 x - 28)$. Grouping the first two terms and factoring out their GCF, $3 x^{2}$, gives $3 x^{2}(x + 7)$. Grouping the last two terms and factoring out their GCF, $-4$, gives $-4(x + 7)$. The polynomial now has a common binomial factor of $x + 7$. This gives $-2[3 x^{2} \left(x + 7\right) -4 \cdot \left(x + 7\right)] = -2\left(x + 7\right) \left(3 x^{2} - 4\right)$. }

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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HTML for Canvas 
<p> <p>Factor  <img class="equation_image" title=" \displaystyle - 6 x^{3} - 42 x^{2} + 8 x + 56 " src="/equation_images/%20%5Cdisplaystyle%20-%206%20x%5E%7B3%7D%20-%2042%20x%5E%7B2%7D%20%2B%208%20x%20%2B%2056%20" alt="LaTeX:  \displaystyle - 6 x^{3} - 42 x^{2} + 8 x + 56 " data-equation-content=" \displaystyle - 6 x^{3} - 42 x^{2} + 8 x + 56 " /> . </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(3 x^{3} + 21 x^{2} - 4 x - 28) " src="/equation_images/%20%5Cdisplaystyle%20-2%283%20x%5E%7B3%7D%20%2B%2021%20x%5E%7B2%7D%20-%204%20x%20-%2028%29%20" alt="LaTeX:  \displaystyle -2(3 x^{3} + 21 x^{2} - 4 x - 28) " data-equation-content=" \displaystyle -2(3 x^{3} + 21 x^{2} - 4 x - 28) " /> . 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}(x + 7) " src="/equation_images/%20%5Cdisplaystyle%203%20x%5E%7B2%7D%28x%20%2B%207%29%20" alt="LaTeX:  \displaystyle 3 x^{2}(x + 7) " data-equation-content=" \displaystyle 3 x^{2}(x + 7) " /> . Grouping the last two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle -4 " src="/equation_images/%20%5Cdisplaystyle%20-4%20" alt="LaTeX:  \displaystyle -4 " data-equation-content=" \displaystyle -4 " /> , gives  <img class="equation_image" title=" \displaystyle -4(x + 7) " src="/equation_images/%20%5Cdisplaystyle%20-4%28x%20%2B%207%29%20" alt="LaTeX:  \displaystyle -4(x + 7) " data-equation-content=" \displaystyle -4(x + 7) " /> . The polynomial now has a common binomial factor of  <img class="equation_image" title=" \displaystyle x + 7 " src="/equation_images/%20%5Cdisplaystyle%20x%20%2B%207%20" alt="LaTeX:  \displaystyle x + 7 " data-equation-content=" \displaystyle x + 7 " /> . This gives  <img class="equation_image" title=" \displaystyle -2[3 x^{2} \left(x + 7\right) -4 \cdot \left(x + 7\right)] = -2\left(x + 7\right) \left(3 x^{2} - 4\right) " src="/equation_images/%20%5Cdisplaystyle%20-2%5B3%20x%5E%7B2%7D%20%5Cleft%28x%20%2B%207%5Cright%29%20-4%20%5Ccdot%20%5Cleft%28x%20%2B%207%5Cright%29%5D%20%3D%20-2%5Cleft%28x%20%2B%207%5Cright%29%20%5Cleft%283%20x%5E%7B2%7D%20-%204%5Cright%29%20" alt="LaTeX:  \displaystyle -2[3 x^{2} \left(x + 7\right) -4 \cdot \left(x + 7\right)] = -2\left(x + 7\right) \left(3 x^{2} - 4\right) " data-equation-content=" \displaystyle -2[3 x^{2} \left(x + 7\right) -4 \cdot \left(x + 7\right)] = -2\left(x + 7\right) \left(3 x^{2} - 4\right) " /> . </p> </p>