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Factor \(\displaystyle 9 x^{3} - 36 x^{2} - 10 x + 40\).

Grouping the first two terms and factoring out their GCF, \(\displaystyle 9 x^{2}\), gives \(\displaystyle 9 x^{2}(x - 4)\). Grouping the last two terms and factoring out their GCF, \(\displaystyle -10\), gives \(\displaystyle -10(x - 4)\). The polynomial now has a common binomial factor of \(\displaystyle x - 4\). This gives \(\displaystyle 9 x^{2} \left(x - 4\right) -10 \cdot \left(x - 4\right) = \left(x - 4\right) \left(9 x^{2} - 10\right)\).

Download \(\LaTeX\) 

\begin{question}Factor $9 x^{3} - 36 x^{2} - 10 x + 40$. 
    \soln{9cm}{Grouping the first two terms and factoring out their GCF, $9 x^{2}$, gives $9 x^{2}(x - 4)$. Grouping the last two terms and factoring out their GCF, $-10$, gives $-10(x - 4)$. The polynomial now has a common binomial factor of $x - 4$. This gives $9 x^{2} \left(x - 4\right) -10 \cdot \left(x - 4\right) = \left(x - 4\right) \left(9 x^{2} - 10\right)$. }

\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 9 x^{3} - 36 x^{2} - 10 x + 40 " src="/equation_images/%20%5Cdisplaystyle%209%20x%5E%7B3%7D%20-%2036%20x%5E%7B2%7D%20-%2010%20x%20%2B%2040%20" alt="LaTeX:  \displaystyle 9 x^{3} - 36 x^{2} - 10 x + 40 " data-equation-content=" \displaystyle 9 x^{3} - 36 x^{2} - 10 x + 40 " /> . </p> </p>
HTML for Canvas
<p> <p>Grouping the first two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle 9 x^{2} " src="/equation_images/%20%5Cdisplaystyle%209%20x%5E%7B2%7D%20" alt="LaTeX:  \displaystyle 9 x^{2} " data-equation-content=" \displaystyle 9 x^{2} " /> , gives  <img class="equation_image" title=" \displaystyle 9 x^{2}(x - 4) " src="/equation_images/%20%5Cdisplaystyle%209%20x%5E%7B2%7D%28x%20-%204%29%20" alt="LaTeX:  \displaystyle 9 x^{2}(x - 4) " data-equation-content=" \displaystyle 9 x^{2}(x - 4) " /> . Grouping the last two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle -10 " src="/equation_images/%20%5Cdisplaystyle%20-10%20" alt="LaTeX:  \displaystyle -10 " data-equation-content=" \displaystyle -10 " /> , gives  <img class="equation_image" title=" \displaystyle -10(x - 4) " src="/equation_images/%20%5Cdisplaystyle%20-10%28x%20-%204%29%20" alt="LaTeX:  \displaystyle -10(x - 4) " data-equation-content=" \displaystyle -10(x - 4) " /> . The polynomial now has a common binomial factor of  <img class="equation_image" title=" \displaystyle x - 4 " src="/equation_images/%20%5Cdisplaystyle%20x%20-%204%20" alt="LaTeX:  \displaystyle x - 4 " data-equation-content=" \displaystyle x - 4 " /> . This gives  <img class="equation_image" title=" \displaystyle 9 x^{2} \left(x - 4\right) -10 \cdot \left(x - 4\right) = \left(x - 4\right) \left(9 x^{2} - 10\right) " src="/equation_images/%20%5Cdisplaystyle%209%20x%5E%7B2%7D%20%5Cleft%28x%20-%204%5Cright%29%20-10%20%5Ccdot%20%5Cleft%28x%20-%204%5Cright%29%20%3D%20%5Cleft%28x%20-%204%5Cright%29%20%5Cleft%289%20x%5E%7B2%7D%20-%2010%5Cright%29%20" alt="LaTeX:  \displaystyle 9 x^{2} \left(x - 4\right) -10 \cdot \left(x - 4\right) = \left(x - 4\right) \left(9 x^{2} - 10\right) " data-equation-content=" \displaystyle 9 x^{2} \left(x - 4\right) -10 \cdot \left(x - 4\right) = \left(x - 4\right) \left(9 x^{2} - 10\right) " /> . </p> </p>