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Factor \(\displaystyle - 63 x^{3} + 7 x^{2} - 72 x + 8\).

Factoring out the GCF \(\displaystyle -1\) from each term gives \(\displaystyle -(63 x^{3} - 7 x^{2} + 72 x - 8)\). Grouping the first two terms and factoring out their GCF, \(\displaystyle 7 x^{2}\), gives \(\displaystyle 7 x^{2}(9 x - 1)\). Grouping the last two terms and factoring out their GCF, \(\displaystyle 8\), gives \(\displaystyle 8(9 x - 1)\). The polynomial now has a common binomial factor of \(\displaystyle 9 x - 1\). This gives \(\displaystyle -1[7 x^{2} \left(9 x - 1\right) +8 \cdot \left(9 x - 1\right)] = -\left(9 x - 1\right) \left(7 x^{2} + 8\right)\).

Download \(\LaTeX\) 

\begin{question}Factor $- 63 x^{3} + 7 x^{2} - 72 x + 8$. 
    \soln{9cm}{Factoring out the GCF $-1$ from each term gives $-(63 x^{3} - 7 x^{2} + 72 x - 8)$. Grouping the first two terms and factoring out their GCF, $7 x^{2}$, gives $7 x^{2}(9 x - 1)$. Grouping the last two terms and factoring out their GCF, $8$, gives $8(9 x - 1)$. The polynomial now has a common binomial factor of $9 x - 1$. This gives $-1[7 x^{2} \left(9 x - 1\right) +8 \cdot \left(9 x - 1\right)] = -\left(9 x - 1\right) \left(7 x^{2} + 8\right)$. }

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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HTML for Canvas 
<p> <p>Factor  <img class="equation_image" title=" \displaystyle - 63 x^{3} + 7 x^{2} - 72 x + 8 " src="/equation_images/%20%5Cdisplaystyle%20-%2063%20x%5E%7B3%7D%20%2B%207%20x%5E%7B2%7D%20-%2072%20x%20%2B%208%20" alt="LaTeX:  \displaystyle - 63 x^{3} + 7 x^{2} - 72 x + 8 " data-equation-content=" \displaystyle - 63 x^{3} + 7 x^{2} - 72 x + 8 " /> . </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 -(63 x^{3} - 7 x^{2} + 72 x - 8) " src="/equation_images/%20%5Cdisplaystyle%20-%2863%20x%5E%7B3%7D%20-%207%20x%5E%7B2%7D%20%2B%2072%20x%20-%208%29%20" alt="LaTeX:  \displaystyle -(63 x^{3} - 7 x^{2} + 72 x - 8) " data-equation-content=" \displaystyle -(63 x^{3} - 7 x^{2} + 72 x - 8) " /> . 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}(9 x - 1) " src="/equation_images/%20%5Cdisplaystyle%207%20x%5E%7B2%7D%289%20x%20-%201%29%20" alt="LaTeX:  \displaystyle 7 x^{2}(9 x - 1) " data-equation-content=" \displaystyle 7 x^{2}(9 x - 1) " /> . Grouping the last two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle 8 " src="/equation_images/%20%5Cdisplaystyle%208%20" alt="LaTeX:  \displaystyle 8 " data-equation-content=" \displaystyle 8 " /> , gives  <img class="equation_image" title=" \displaystyle 8(9 x - 1) " src="/equation_images/%20%5Cdisplaystyle%208%289%20x%20-%201%29%20" alt="LaTeX:  \displaystyle 8(9 x - 1) " data-equation-content=" \displaystyle 8(9 x - 1) " /> . The polynomial now has a common binomial factor of  <img class="equation_image" title=" \displaystyle 9 x - 1 " src="/equation_images/%20%5Cdisplaystyle%209%20x%20-%201%20" alt="LaTeX:  \displaystyle 9 x - 1 " data-equation-content=" \displaystyle 9 x - 1 " /> . This gives  <img class="equation_image" title=" \displaystyle -1[7 x^{2} \left(9 x - 1\right) +8 \cdot \left(9 x - 1\right)] = -\left(9 x - 1\right) \left(7 x^{2} + 8\right) " src="/equation_images/%20%5Cdisplaystyle%20-1%5B7%20x%5E%7B2%7D%20%5Cleft%289%20x%20-%201%5Cright%29%20%2B8%20%5Ccdot%20%5Cleft%289%20x%20-%201%5Cright%29%5D%20%3D%20-%5Cleft%289%20x%20-%201%5Cright%29%20%5Cleft%287%20x%5E%7B2%7D%20%2B%208%5Cright%29%20" alt="LaTeX:  \displaystyle -1[7 x^{2} \left(9 x - 1\right) +8 \cdot \left(9 x - 1\right)] = -\left(9 x - 1\right) \left(7 x^{2} + 8\right) " data-equation-content=" \displaystyle -1[7 x^{2} \left(9 x - 1\right) +8 \cdot \left(9 x - 1\right)] = -\left(9 x - 1\right) \left(7 x^{2} + 8\right) " /> . </p> </p>