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Factor \(\displaystyle - 80 x^{3} + 10 x^{2} - 40 x + 5\).

Factoring out the GCF \(\displaystyle -5\) from each term gives \(\displaystyle -5(16 x^{3} - 2 x^{2} + 8 x - 1)\). Grouping the first two terms and factoring out their GCF, \(\displaystyle 2 x^{2}\), gives \(\displaystyle 2 x^{2}(8 x - 1)\). Grouping the last two terms and factoring out their GCF, \(\displaystyle 1\), gives \(\displaystyle 1(8 x - 1)\). The polynomial now has a common binomial factor of \(\displaystyle 8 x - 1\). This gives \(\displaystyle -5[2 x^{2} \left(8 x - 1\right) +1 \cdot \left(8 x - 1\right)] = -5\left(8 x - 1\right) \left(2 x^{2} + 1\right)\).

Download \(\LaTeX\) 

\begin{question}Factor $- 80 x^{3} + 10 x^{2} - 40 x + 5$. 
    \soln{9cm}{Factoring out the GCF $-5$ from each term gives $-5(16 x^{3} - 2 x^{2} + 8 x - 1)$. Grouping the first two terms and factoring out their GCF, $2 x^{2}$, gives $2 x^{2}(8 x - 1)$. Grouping the last two terms and factoring out their GCF, $1$, gives $1(8 x - 1)$. The polynomial now has a common binomial factor of $8 x - 1$. This gives $-5[2 x^{2} \left(8 x - 1\right) +1 \cdot \left(8 x - 1\right)] = -5\left(8 x - 1\right) \left(2 x^{2} + 1\right)$. }

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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HTML for Canvas 
<p> <p>Factor  <img class="equation_image" title=" \displaystyle - 80 x^{3} + 10 x^{2} - 40 x + 5 " src="/equation_images/%20%5Cdisplaystyle%20-%2080%20x%5E%7B3%7D%20%2B%2010%20x%5E%7B2%7D%20-%2040%20x%20%2B%205%20" alt="LaTeX:  \displaystyle - 80 x^{3} + 10 x^{2} - 40 x + 5 " data-equation-content=" \displaystyle - 80 x^{3} + 10 x^{2} - 40 x + 5 " /> . </p> </p>
HTML for Canvas
<p> <p>Factoring out the GCF  <img class="equation_image" title=" \displaystyle -5 " src="/equation_images/%20%5Cdisplaystyle%20-5%20" alt="LaTeX:  \displaystyle -5 " data-equation-content=" \displaystyle -5 " />  from each term gives  <img class="equation_image" title=" \displaystyle -5(16 x^{3} - 2 x^{2} + 8 x - 1) " src="/equation_images/%20%5Cdisplaystyle%20-5%2816%20x%5E%7B3%7D%20-%202%20x%5E%7B2%7D%20%2B%208%20x%20-%201%29%20" alt="LaTeX:  \displaystyle -5(16 x^{3} - 2 x^{2} + 8 x - 1) " data-equation-content=" \displaystyle -5(16 x^{3} - 2 x^{2} + 8 x - 1) " /> . Grouping the first two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle 2 x^{2} " src="/equation_images/%20%5Cdisplaystyle%202%20x%5E%7B2%7D%20" alt="LaTeX:  \displaystyle 2 x^{2} " data-equation-content=" \displaystyle 2 x^{2} " /> , gives  <img class="equation_image" title=" \displaystyle 2 x^{2}(8 x - 1) " src="/equation_images/%20%5Cdisplaystyle%202%20x%5E%7B2%7D%288%20x%20-%201%29%20" alt="LaTeX:  \displaystyle 2 x^{2}(8 x - 1) " data-equation-content=" \displaystyle 2 x^{2}(8 x - 1) " /> . 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(8 x - 1) " src="/equation_images/%20%5Cdisplaystyle%201%288%20x%20-%201%29%20" alt="LaTeX:  \displaystyle 1(8 x - 1) " data-equation-content=" \displaystyle 1(8 x - 1) " /> . The polynomial now has a common binomial factor of  <img class="equation_image" title=" \displaystyle 8 x - 1 " src="/equation_images/%20%5Cdisplaystyle%208%20x%20-%201%20" alt="LaTeX:  \displaystyle 8 x - 1 " data-equation-content=" \displaystyle 8 x - 1 " /> . This gives  <img class="equation_image" title=" \displaystyle -5[2 x^{2} \left(8 x - 1\right) +1 \cdot \left(8 x - 1\right)] = -5\left(8 x - 1\right) \left(2 x^{2} + 1\right) " src="/equation_images/%20%5Cdisplaystyle%20-5%5B2%20x%5E%7B2%7D%20%5Cleft%288%20x%20-%201%5Cright%29%20%2B1%20%5Ccdot%20%5Cleft%288%20x%20-%201%5Cright%29%5D%20%3D%20-5%5Cleft%288%20x%20-%201%5Cright%29%20%5Cleft%282%20x%5E%7B2%7D%20%2B%201%5Cright%29%20" alt="LaTeX:  \displaystyle -5[2 x^{2} \left(8 x - 1\right) +1 \cdot \left(8 x - 1\right)] = -5\left(8 x - 1\right) \left(2 x^{2} + 1\right) " data-equation-content=" \displaystyle -5[2 x^{2} \left(8 x - 1\right) +1 \cdot \left(8 x - 1\right)] = -5\left(8 x - 1\right) \left(2 x^{2} + 1\right) " /> . </p> </p>