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Factor \(\displaystyle - 16 x^{3} + 80 x^{2} - 2 x + 10\).

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

Download \(\LaTeX\) 

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

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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HTML for Canvas 
<p> <p>Factor  <img class="equation_image" title=" \displaystyle - 16 x^{3} + 80 x^{2} - 2 x + 10 " src="/equation_images/%20%5Cdisplaystyle%20-%2016%20x%5E%7B3%7D%20%2B%2080%20x%5E%7B2%7D%20-%202%20x%20%2B%2010%20" alt="LaTeX:  \displaystyle - 16 x^{3} + 80 x^{2} - 2 x + 10 " data-equation-content=" \displaystyle - 16 x^{3} + 80 x^{2} - 2 x + 10 " /> . </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(8 x^{3} - 40 x^{2} + x - 5) " src="/equation_images/%20%5Cdisplaystyle%20-2%288%20x%5E%7B3%7D%20-%2040%20x%5E%7B2%7D%20%2B%20x%20-%205%29%20" alt="LaTeX:  \displaystyle -2(8 x^{3} - 40 x^{2} + x - 5) " data-equation-content=" \displaystyle -2(8 x^{3} - 40 x^{2} + x - 5) " /> . 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}(x - 5) " src="/equation_images/%20%5Cdisplaystyle%208%20x%5E%7B2%7D%28x%20-%205%29%20" alt="LaTeX:  \displaystyle 8 x^{2}(x - 5) " data-equation-content=" \displaystyle 8 x^{2}(x - 5) " /> . 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(x - 5) " src="/equation_images/%20%5Cdisplaystyle%201%28x%20-%205%29%20" alt="LaTeX:  \displaystyle 1(x - 5) " data-equation-content=" \displaystyle 1(x - 5) " /> . The polynomial now has a common binomial factor of  <img class="equation_image" title=" \displaystyle x - 5 " src="/equation_images/%20%5Cdisplaystyle%20x%20-%205%20" alt="LaTeX:  \displaystyle x - 5 " data-equation-content=" \displaystyle x - 5 " /> . This gives  <img class="equation_image" title=" \displaystyle -2[8 x^{2} \left(x - 5\right) +1 \cdot \left(x - 5\right)] = -2\left(x - 5\right) \left(8 x^{2} + 1\right) " src="/equation_images/%20%5Cdisplaystyle%20-2%5B8%20x%5E%7B2%7D%20%5Cleft%28x%20-%205%5Cright%29%20%2B1%20%5Ccdot%20%5Cleft%28x%20-%205%5Cright%29%5D%20%3D%20-2%5Cleft%28x%20-%205%5Cright%29%20%5Cleft%288%20x%5E%7B2%7D%20%2B%201%5Cright%29%20" alt="LaTeX:  \displaystyle -2[8 x^{2} \left(x - 5\right) +1 \cdot \left(x - 5\right)] = -2\left(x - 5\right) \left(8 x^{2} + 1\right) " data-equation-content=" \displaystyle -2[8 x^{2} \left(x - 5\right) +1 \cdot \left(x - 5\right)] = -2\left(x - 5\right) \left(8 x^{2} + 1\right) " /> . </p> </p>