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Factor \(\displaystyle - 25 x^{3} + 45 x^{2} + 20 x - 36\).

Factoring out the GCF \(\displaystyle -1\) from each term gives \(\displaystyle -(25 x^{3} - 45 x^{2} - 20 x + 36)\). Grouping the first two terms and factoring out their GCF, \(\displaystyle 5 x^{2}\), gives \(\displaystyle 5 x^{2}(5 x - 9)\). Grouping the last two terms and factoring out their GCF, \(\displaystyle -4\), gives \(\displaystyle -4(5 x - 9)\). The polynomial now has a common binomial factor of \(\displaystyle 5 x - 9\). This gives \(\displaystyle -1[5 x^{2} \left(5 x - 9\right) -4 \cdot \left(5 x - 9\right)] = -\left(5 x - 9\right) \left(5 x^{2} - 4\right)\).

Download \(\LaTeX\) 

\begin{question}Factor $- 25 x^{3} + 45 x^{2} + 20 x - 36$. 
    \soln{9cm}{Factoring out the GCF $-1$ from each term gives $-(25 x^{3} - 45 x^{2} - 20 x + 36)$. Grouping the first two terms and factoring out their GCF, $5 x^{2}$, gives $5 x^{2}(5 x - 9)$. Grouping the last two terms and factoring out their GCF, $-4$, gives $-4(5 x - 9)$. The polynomial now has a common binomial factor of $5 x - 9$. This gives $-1[5 x^{2} \left(5 x - 9\right) -4 \cdot \left(5 x - 9\right)] = -\left(5 x - 9\right) \left(5 x^{2} - 4\right)$. }

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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HTML for Canvas 
<p> <p>Factor  <img class="equation_image" title=" \displaystyle - 25 x^{3} + 45 x^{2} + 20 x - 36 " src="/equation_images/%20%5Cdisplaystyle%20-%2025%20x%5E%7B3%7D%20%2B%2045%20x%5E%7B2%7D%20%2B%2020%20x%20-%2036%20" alt="LaTeX:  \displaystyle - 25 x^{3} + 45 x^{2} + 20 x - 36 " data-equation-content=" \displaystyle - 25 x^{3} + 45 x^{2} + 20 x - 36 " /> . </p> </p>
HTML for Canvas
<p> <p>Factoring out the GCF  <img class="equation_image" title=" \displaystyle -1 " src="/equation_images/%20%5Cdisplaystyle%20-1%20" alt="LaTeX:  \displaystyle -1 " data-equation-content=" \displaystyle -1 " />  from each term gives  <img class="equation_image" title=" \displaystyle -(25 x^{3} - 45 x^{2} - 20 x + 36) " src="/equation_images/%20%5Cdisplaystyle%20-%2825%20x%5E%7B3%7D%20-%2045%20x%5E%7B2%7D%20-%2020%20x%20%2B%2036%29%20" alt="LaTeX:  \displaystyle -(25 x^{3} - 45 x^{2} - 20 x + 36) " data-equation-content=" \displaystyle -(25 x^{3} - 45 x^{2} - 20 x + 36) " /> . Grouping the first two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle 5 x^{2} " src="/equation_images/%20%5Cdisplaystyle%205%20x%5E%7B2%7D%20" alt="LaTeX:  \displaystyle 5 x^{2} " data-equation-content=" \displaystyle 5 x^{2} " /> , gives  <img class="equation_image" title=" \displaystyle 5 x^{2}(5 x - 9) " src="/equation_images/%20%5Cdisplaystyle%205%20x%5E%7B2%7D%285%20x%20-%209%29%20" alt="LaTeX:  \displaystyle 5 x^{2}(5 x - 9) " data-equation-content=" \displaystyle 5 x^{2}(5 x - 9) " /> . Grouping the last two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle -4 " src="/equation_images/%20%5Cdisplaystyle%20-4%20" alt="LaTeX:  \displaystyle -4 " data-equation-content=" \displaystyle -4 " /> , gives  <img class="equation_image" title=" \displaystyle -4(5 x - 9) " src="/equation_images/%20%5Cdisplaystyle%20-4%285%20x%20-%209%29%20" alt="LaTeX:  \displaystyle -4(5 x - 9) " data-equation-content=" \displaystyle -4(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 -1[5 x^{2} \left(5 x - 9\right) -4 \cdot \left(5 x - 9\right)] = -\left(5 x - 9\right) \left(5 x^{2} - 4\right) " src="/equation_images/%20%5Cdisplaystyle%20-1%5B5%20x%5E%7B2%7D%20%5Cleft%285%20x%20-%209%5Cright%29%20-4%20%5Ccdot%20%5Cleft%285%20x%20-%209%5Cright%29%5D%20%3D%20-%5Cleft%285%20x%20-%209%5Cright%29%20%5Cleft%285%20x%5E%7B2%7D%20-%204%5Cright%29%20" alt="LaTeX:  \displaystyle -1[5 x^{2} \left(5 x - 9\right) -4 \cdot \left(5 x - 9\right)] = -\left(5 x - 9\right) \left(5 x^{2} - 4\right) " data-equation-content=" \displaystyle -1[5 x^{2} \left(5 x - 9\right) -4 \cdot \left(5 x - 9\right)] = -\left(5 x - 9\right) \left(5 x^{2} - 4\right) " /> . </p> </p>