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Factor \(\displaystyle - 20 x^{3} - 16 x^{2} + 90 x + 72\).

Factoring out the GCF \(\displaystyle -2\) from each term gives \(\displaystyle -2(10 x^{3} + 8 x^{2} - 45 x - 36)\). Grouping the first two terms and factoring out their GCF, \(\displaystyle 2 x^{2}\), gives \(\displaystyle 2 x^{2}(5 x + 4)\). Grouping the last two terms and factoring out their GCF, \(\displaystyle -9\), gives \(\displaystyle -9(5 x + 4)\). The polynomial now has a common binomial factor of \(\displaystyle 5 x + 4\). This gives \(\displaystyle -2[2 x^{2} \left(5 x + 4\right) -9 \cdot \left(5 x + 4\right)] = -2\left(5 x + 4\right) \left(2 x^{2} - 9\right)\).

Download \(\LaTeX\) 

\begin{question}Factor $- 20 x^{3} - 16 x^{2} + 90 x + 72$. 
    \soln{9cm}{Factoring out the GCF $-2$ from each term gives $-2(10 x^{3} + 8 x^{2} - 45 x - 36)$. Grouping the first two terms and factoring out their GCF, $2 x^{2}$, gives $2 x^{2}(5 x + 4)$. Grouping the last two terms and factoring out their GCF, $-9$, gives $-9(5 x + 4)$. The polynomial now has a common binomial factor of $5 x + 4$. This gives $-2[2 x^{2} \left(5 x + 4\right) -9 \cdot \left(5 x + 4\right)] = -2\left(5 x + 4\right) \left(2 x^{2} - 9\right)$. }

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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HTML for Canvas 
<p> <p>Factor  <img class="equation_image" title=" \displaystyle - 20 x^{3} - 16 x^{2} + 90 x + 72 " src="/equation_images/%20%5Cdisplaystyle%20-%2020%20x%5E%7B3%7D%20-%2016%20x%5E%7B2%7D%20%2B%2090%20x%20%2B%2072%20" alt="LaTeX:  \displaystyle - 20 x^{3} - 16 x^{2} + 90 x + 72 " data-equation-content=" \displaystyle - 20 x^{3} - 16 x^{2} + 90 x + 72 " /> . </p> </p>
HTML for Canvas
<p> <p>Factoring out the GCF  <img class="equation_image" title=" \displaystyle -2 " src="/equation_images/%20%5Cdisplaystyle%20-2%20" alt="LaTeX:  \displaystyle -2 " data-equation-content=" \displaystyle -2 " />  from each term gives  <img class="equation_image" title=" \displaystyle -2(10 x^{3} + 8 x^{2} - 45 x - 36) " src="/equation_images/%20%5Cdisplaystyle%20-2%2810%20x%5E%7B3%7D%20%2B%208%20x%5E%7B2%7D%20-%2045%20x%20-%2036%29%20" alt="LaTeX:  \displaystyle -2(10 x^{3} + 8 x^{2} - 45 x - 36) " data-equation-content=" \displaystyle -2(10 x^{3} + 8 x^{2} - 45 x - 36) " /> . 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 + 4) " src="/equation_images/%20%5Cdisplaystyle%202%20x%5E%7B2%7D%285%20x%20%2B%204%29%20" alt="LaTeX:  \displaystyle 2 x^{2}(5 x + 4) " data-equation-content=" \displaystyle 2 x^{2}(5 x + 4) " /> . Grouping the last two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle -9 " src="/equation_images/%20%5Cdisplaystyle%20-9%20" alt="LaTeX:  \displaystyle -9 " data-equation-content=" \displaystyle -9 " /> , gives  <img class="equation_image" title=" \displaystyle -9(5 x + 4) " src="/equation_images/%20%5Cdisplaystyle%20-9%285%20x%20%2B%204%29%20" alt="LaTeX:  \displaystyle -9(5 x + 4) " data-equation-content=" \displaystyle -9(5 x + 4) " /> . The polynomial now has a common binomial factor of  <img class="equation_image" title=" \displaystyle 5 x + 4 " src="/equation_images/%20%5Cdisplaystyle%205%20x%20%2B%204%20" alt="LaTeX:  \displaystyle 5 x + 4 " data-equation-content=" \displaystyle 5 x + 4 " /> . This gives  <img class="equation_image" title=" \displaystyle -2[2 x^{2} \left(5 x + 4\right) -9 \cdot \left(5 x + 4\right)] = -2\left(5 x + 4\right) \left(2 x^{2} - 9\right) " src="/equation_images/%20%5Cdisplaystyle%20-2%5B2%20x%5E%7B2%7D%20%5Cleft%285%20x%20%2B%204%5Cright%29%20-9%20%5Ccdot%20%5Cleft%285%20x%20%2B%204%5Cright%29%5D%20%3D%20-2%5Cleft%285%20x%20%2B%204%5Cright%29%20%5Cleft%282%20x%5E%7B2%7D%20-%209%5Cright%29%20" alt="LaTeX:  \displaystyle -2[2 x^{2} \left(5 x + 4\right) -9 \cdot \left(5 x + 4\right)] = -2\left(5 x + 4\right) \left(2 x^{2} - 9\right) " data-equation-content=" \displaystyle -2[2 x^{2} \left(5 x + 4\right) -9 \cdot \left(5 x + 4\right)] = -2\left(5 x + 4\right) \left(2 x^{2} - 9\right) " /> . </p> </p>