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Factor \(\displaystyle 80 x^{3} - 48 x^{2} + 40 x - 24\).

Factoring out the GCF \(\displaystyle 8\) from each term gives \(\displaystyle 8(10 x^{3} - 6 x^{2} + 5 x - 3)\). Grouping the first two terms and factoring out their GCF, \(\displaystyle 2 x^{2}\), gives \(\displaystyle 2 x^{2}(5 x - 3)\). Grouping the last two terms and factoring out their GCF, \(\displaystyle 1\), gives \(\displaystyle 1(5 x - 3)\). The polynomial now has a common binomial factor of \(\displaystyle 5 x - 3\). This gives \(\displaystyle 8[2 x^{2} \left(5 x - 3\right) +1 \cdot \left(5 x - 3\right)] = 8\left(5 x - 3\right) \left(2 x^{2} + 1\right)\).

Download \(\LaTeX\) 

\begin{question}Factor $80 x^{3} - 48 x^{2} + 40 x - 24$. 
    \soln{9cm}{Factoring out the GCF $8$ from each term gives $8(10 x^{3} - 6 x^{2} + 5 x - 3)$. Grouping the first two terms and factoring out their GCF, $2 x^{2}$, gives $2 x^{2}(5 x - 3)$. Grouping the last two terms and factoring out their GCF, $1$, gives $1(5 x - 3)$. The polynomial now has a common binomial factor of $5 x - 3$. This gives $8[2 x^{2} \left(5 x - 3\right) +1 \cdot \left(5 x - 3\right)] = 8\left(5 x - 3\right) \left(2 x^{2} + 1\right)$. }

\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} - 48 x^{2} + 40 x - 24 " src="/equation_images/%20%5Cdisplaystyle%2080%20x%5E%7B3%7D%20-%2048%20x%5E%7B2%7D%20%2B%2040%20x%20-%2024%20" alt="LaTeX:  \displaystyle 80 x^{3} - 48 x^{2} + 40 x - 24 " data-equation-content=" \displaystyle 80 x^{3} - 48 x^{2} + 40 x - 24 " /> . </p> </p>
HTML for Canvas
<p> <p>Factoring out the GCF  <img class="equation_image" title=" \displaystyle 8 " src="/equation_images/%20%5Cdisplaystyle%208%20" alt="LaTeX:  \displaystyle 8 " data-equation-content=" \displaystyle 8 " />  from each term gives  <img class="equation_image" title=" \displaystyle 8(10 x^{3} - 6 x^{2} + 5 x - 3) " src="/equation_images/%20%5Cdisplaystyle%208%2810%20x%5E%7B3%7D%20-%206%20x%5E%7B2%7D%20%2B%205%20x%20-%203%29%20" alt="LaTeX:  \displaystyle 8(10 x^{3} - 6 x^{2} + 5 x - 3) " data-equation-content=" \displaystyle 8(10 x^{3} - 6 x^{2} + 5 x - 3) " /> . 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}(5 x - 3) " src="/equation_images/%20%5Cdisplaystyle%202%20x%5E%7B2%7D%285%20x%20-%203%29%20" alt="LaTeX:  \displaystyle 2 x^{2}(5 x - 3) " data-equation-content=" \displaystyle 2 x^{2}(5 x - 3) " /> . 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(5 x - 3) " src="/equation_images/%20%5Cdisplaystyle%201%285%20x%20-%203%29%20" alt="LaTeX:  \displaystyle 1(5 x - 3) " data-equation-content=" \displaystyle 1(5 x - 3) " /> . The polynomial now has a common binomial factor of  <img class="equation_image" title=" \displaystyle 5 x - 3 " src="/equation_images/%20%5Cdisplaystyle%205%20x%20-%203%20" alt="LaTeX:  \displaystyle 5 x - 3 " data-equation-content=" \displaystyle 5 x - 3 " /> . This gives  <img class="equation_image" title=" \displaystyle 8[2 x^{2} \left(5 x - 3\right) +1 \cdot \left(5 x - 3\right)] = 8\left(5 x - 3\right) \left(2 x^{2} + 1\right) " src="/equation_images/%20%5Cdisplaystyle%208%5B2%20x%5E%7B2%7D%20%5Cleft%285%20x%20-%203%5Cright%29%20%2B1%20%5Ccdot%20%5Cleft%285%20x%20-%203%5Cright%29%5D%20%3D%208%5Cleft%285%20x%20-%203%5Cright%29%20%5Cleft%282%20x%5E%7B2%7D%20%2B%201%5Cright%29%20" alt="LaTeX:  \displaystyle 8[2 x^{2} \left(5 x - 3\right) +1 \cdot \left(5 x - 3\right)] = 8\left(5 x - 3\right) \left(2 x^{2} + 1\right) " data-equation-content=" \displaystyle 8[2 x^{2} \left(5 x - 3\right) +1 \cdot \left(5 x - 3\right)] = 8\left(5 x - 3\right) \left(2 x^{2} + 1\right) " /> . </p> </p>