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Factor \(\displaystyle 50 x^{3} - 10 x^{2} - 80 x + 16\).

Factoring out the GCF \(\displaystyle 2\) from each term gives \(\displaystyle 2(25 x^{3} - 5 x^{2} - 40 x + 8)\). Grouping the first two terms and factoring out their GCF, \(\displaystyle 5 x^{2}\), gives \(\displaystyle 5 x^{2}(5 x - 1)\). Grouping the last two terms and factoring out their GCF, \(\displaystyle -8\), gives \(\displaystyle -8(5 x - 1)\). The polynomial now has a common binomial factor of \(\displaystyle 5 x - 1\). This gives \(\displaystyle 2[5 x^{2} \left(5 x - 1\right) -8 \cdot \left(5 x - 1\right)] = 2\left(5 x - 1\right) \left(5 x^{2} - 8\right)\).

Download \(\LaTeX\) 

\begin{question}Factor $50 x^{3} - 10 x^{2} - 80 x + 16$. 
    \soln{9cm}{Factoring out the GCF $2$ from each term gives $2(25 x^{3} - 5 x^{2} - 40 x + 8)$. Grouping the first two terms and factoring out their GCF, $5 x^{2}$, gives $5 x^{2}(5 x - 1)$. Grouping the last two terms and factoring out their GCF, $-8$, gives $-8(5 x - 1)$. The polynomial now has a common binomial factor of $5 x - 1$. This gives $2[5 x^{2} \left(5 x - 1\right) -8 \cdot \left(5 x - 1\right)] = 2\left(5 x - 1\right) \left(5 x^{2} - 8\right)$. }

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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HTML for Canvas 
<p> <p>Factor  <img class="equation_image" title=" \displaystyle 50 x^{3} - 10 x^{2} - 80 x + 16 " src="/equation_images/%20%5Cdisplaystyle%2050%20x%5E%7B3%7D%20-%2010%20x%5E%7B2%7D%20-%2080%20x%20%2B%2016%20" alt="LaTeX:  \displaystyle 50 x^{3} - 10 x^{2} - 80 x + 16 " data-equation-content=" \displaystyle 50 x^{3} - 10 x^{2} - 80 x + 16 " /> . </p> </p>
HTML for Canvas
<p> <p>Factoring out the GCF  <img class="equation_image" title=" \displaystyle 2 " src="/equation_images/%20%5Cdisplaystyle%202%20" alt="LaTeX:  \displaystyle 2 " data-equation-content=" \displaystyle 2 " />  from each term gives  <img class="equation_image" title=" \displaystyle 2(25 x^{3} - 5 x^{2} - 40 x + 8) " src="/equation_images/%20%5Cdisplaystyle%202%2825%20x%5E%7B3%7D%20-%205%20x%5E%7B2%7D%20-%2040%20x%20%2B%208%29%20" alt="LaTeX:  \displaystyle 2(25 x^{3} - 5 x^{2} - 40 x + 8) " data-equation-content=" \displaystyle 2(25 x^{3} - 5 x^{2} - 40 x + 8) " /> . Grouping the first two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle 5 x^{2} " src="/equation_images/%20%5Cdisplaystyle%205%20x%5E%7B2%7D%20" alt="LaTeX:  \displaystyle 5 x^{2} " data-equation-content=" \displaystyle 5 x^{2} " /> , gives  <img class="equation_image" title=" \displaystyle 5 x^{2}(5 x - 1) " src="/equation_images/%20%5Cdisplaystyle%205%20x%5E%7B2%7D%285%20x%20-%201%29%20" alt="LaTeX:  \displaystyle 5 x^{2}(5 x - 1) " data-equation-content=" \displaystyle 5 x^{2}(5 x - 1) " /> . Grouping the last two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle -8 " src="/equation_images/%20%5Cdisplaystyle%20-8%20" alt="LaTeX:  \displaystyle -8 " data-equation-content=" \displaystyle -8 " /> , gives  <img class="equation_image" title=" \displaystyle -8(5 x - 1) " src="/equation_images/%20%5Cdisplaystyle%20-8%285%20x%20-%201%29%20" alt="LaTeX:  \displaystyle -8(5 x - 1) " data-equation-content=" \displaystyle -8(5 x - 1) " /> . The polynomial now has a common binomial factor of  <img class="equation_image" title=" \displaystyle 5 x - 1 " src="/equation_images/%20%5Cdisplaystyle%205%20x%20-%201%20" alt="LaTeX:  \displaystyle 5 x - 1 " data-equation-content=" \displaystyle 5 x - 1 " /> . This gives  <img class="equation_image" title=" \displaystyle 2[5 x^{2} \left(5 x - 1\right) -8 \cdot \left(5 x - 1\right)] = 2\left(5 x - 1\right) \left(5 x^{2} - 8\right) " src="/equation_images/%20%5Cdisplaystyle%202%5B5%20x%5E%7B2%7D%20%5Cleft%285%20x%20-%201%5Cright%29%20-8%20%5Ccdot%20%5Cleft%285%20x%20-%201%5Cright%29%5D%20%3D%202%5Cleft%285%20x%20-%201%5Cright%29%20%5Cleft%285%20x%5E%7B2%7D%20-%208%5Cright%29%20" alt="LaTeX:  \displaystyle 2[5 x^{2} \left(5 x - 1\right) -8 \cdot \left(5 x - 1\right)] = 2\left(5 x - 1\right) \left(5 x^{2} - 8\right) " data-equation-content=" \displaystyle 2[5 x^{2} \left(5 x - 1\right) -8 \cdot \left(5 x - 1\right)] = 2\left(5 x - 1\right) \left(5 x^{2} - 8\right) " /> . </p> </p>