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Factor \(\displaystyle 8 x^{3} - 16 x^{2} + 5 x - 10\).

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

Download \(\LaTeX\) 

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

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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    \soln{9cm}{The solution goes here.}

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HTML for Canvas 
<p> <p>Factor  <img class="equation_image" title=" \displaystyle 8 x^{3} - 16 x^{2} + 5 x - 10 " src="/equation_images/%20%5Cdisplaystyle%208%20x%5E%7B3%7D%20-%2016%20x%5E%7B2%7D%20%2B%205%20x%20-%2010%20" alt="LaTeX:  \displaystyle 8 x^{3} - 16 x^{2} + 5 x - 10 " data-equation-content=" \displaystyle 8 x^{3} - 16 x^{2} + 5 x - 10 " /> . </p> </p>
HTML for Canvas
<p> <p>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 - 2) " src="/equation_images/%20%5Cdisplaystyle%208%20x%5E%7B2%7D%28x%20-%202%29%20" alt="LaTeX:  \displaystyle 8 x^{2}(x - 2) " data-equation-content=" \displaystyle 8 x^{2}(x - 2) " /> . Grouping the last two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle 5 " src="/equation_images/%20%5Cdisplaystyle%205%20" alt="LaTeX:  \displaystyle 5 " data-equation-content=" \displaystyle 5 " /> , gives  <img class="equation_image" title=" \displaystyle 5(x - 2) " src="/equation_images/%20%5Cdisplaystyle%205%28x%20-%202%29%20" alt="LaTeX:  \displaystyle 5(x - 2) " data-equation-content=" \displaystyle 5(x - 2) " /> . The polynomial now has a common binomial factor of  <img class="equation_image" title=" \displaystyle x - 2 " src="/equation_images/%20%5Cdisplaystyle%20x%20-%202%20" alt="LaTeX:  \displaystyle x - 2 " data-equation-content=" \displaystyle x - 2 " /> . This gives  <img class="equation_image" title=" \displaystyle 8 x^{2} \left(x - 2\right) +5 \cdot \left(x - 2\right) = \left(x - 2\right) \left(8 x^{2} + 5\right) " src="/equation_images/%20%5Cdisplaystyle%208%20x%5E%7B2%7D%20%5Cleft%28x%20-%202%5Cright%29%20%2B5%20%5Ccdot%20%5Cleft%28x%20-%202%5Cright%29%20%3D%20%5Cleft%28x%20-%202%5Cright%29%20%5Cleft%288%20x%5E%7B2%7D%20%2B%205%5Cright%29%20" alt="LaTeX:  \displaystyle 8 x^{2} \left(x - 2\right) +5 \cdot \left(x - 2\right) = \left(x - 2\right) \left(8 x^{2} + 5\right) " data-equation-content=" \displaystyle 8 x^{2} \left(x - 2\right) +5 \cdot \left(x - 2\right) = \left(x - 2\right) \left(8 x^{2} + 5\right) " /> . </p> </p>