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Factor \(\displaystyle 40 x^{3} - 72 x^{2} + 5 x - 9\).

Grouping the first two terms and factoring out their GCF, \(\displaystyle 8 x^{2}\), gives \(\displaystyle 8 x^{2}(5 x - 9)\). Grouping the last two terms and factoring out their GCF, \(\displaystyle 1\), gives \(\displaystyle 1(5 x - 9)\). The polynomial now has a common binomial factor of \(\displaystyle 5 x - 9\). This gives \(\displaystyle 8 x^{2} \left(5 x - 9\right) +1 \cdot \left(5 x - 9\right) = \left(5 x - 9\right) \left(8 x^{2} + 1\right)\).

Download \(\LaTeX\) 

\begin{question}Factor $40 x^{3} - 72 x^{2} + 5 x - 9$. 
    \soln{9cm}{Grouping the first two terms and factoring out their GCF, $8 x^{2}$, gives $8 x^{2}(5 x - 9)$. Grouping the last two terms and factoring out their GCF, $1$, gives $1(5 x - 9)$. The polynomial now has a common binomial factor of $5 x - 9$. This gives $8 x^{2} \left(5 x - 9\right) +1 \cdot \left(5 x - 9\right) = \left(5 x - 9\right) \left(8 x^{2} + 1\right)$. }

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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HTML for Canvas 
<p> <p>Factor  <img class="equation_image" title=" \displaystyle 40 x^{3} - 72 x^{2} + 5 x - 9 " src="/equation_images/%20%5Cdisplaystyle%2040%20x%5E%7B3%7D%20-%2072%20x%5E%7B2%7D%20%2B%205%20x%20-%209%20" alt="LaTeX:  \displaystyle 40 x^{3} - 72 x^{2} + 5 x - 9 " data-equation-content=" \displaystyle 40 x^{3} - 72 x^{2} + 5 x - 9 " /> . </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}(5 x - 9) " src="/equation_images/%20%5Cdisplaystyle%208%20x%5E%7B2%7D%285%20x%20-%209%29%20" alt="LaTeX:  \displaystyle 8 x^{2}(5 x - 9) " data-equation-content=" \displaystyle 8 x^{2}(5 x - 9) " /> . 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 - 9) " src="/equation_images/%20%5Cdisplaystyle%201%285%20x%20-%209%29%20" alt="LaTeX:  \displaystyle 1(5 x - 9) " data-equation-content=" \displaystyle 1(5 x - 9) " /> . The polynomial now has a common binomial factor of  <img class="equation_image" title=" \displaystyle 5 x - 9 " src="/equation_images/%20%5Cdisplaystyle%205%20x%20-%209%20" alt="LaTeX:  \displaystyle 5 x - 9 " data-equation-content=" \displaystyle 5 x - 9 " /> . This gives  <img class="equation_image" title=" \displaystyle 8 x^{2} \left(5 x - 9\right) +1 \cdot \left(5 x - 9\right) = \left(5 x - 9\right) \left(8 x^{2} + 1\right) " src="/equation_images/%20%5Cdisplaystyle%208%20x%5E%7B2%7D%20%5Cleft%285%20x%20-%209%5Cright%29%20%2B1%20%5Ccdot%20%5Cleft%285%20x%20-%209%5Cright%29%20%3D%20%5Cleft%285%20x%20-%209%5Cright%29%20%5Cleft%288%20x%5E%7B2%7D%20%2B%201%5Cright%29%20" alt="LaTeX:  \displaystyle 8 x^{2} \left(5 x - 9\right) +1 \cdot \left(5 x - 9\right) = \left(5 x - 9\right) \left(8 x^{2} + 1\right) " data-equation-content=" \displaystyle 8 x^{2} \left(5 x - 9\right) +1 \cdot \left(5 x - 9\right) = \left(5 x - 9\right) \left(8 x^{2} + 1\right) " /> . </p> </p>