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Factor \(\displaystyle 20 x^{3} + 36 x^{2} - 35 x - 63\).

Grouping the first two terms and factoring out their GCF, \(\displaystyle 4 x^{2}\), gives \(\displaystyle 4 x^{2}(5 x + 9)\). Grouping the last two terms and factoring out their GCF, \(\displaystyle -7\), gives \(\displaystyle -7(5 x + 9)\). The polynomial now has a common binomial factor of \(\displaystyle 5 x + 9\). This gives \(\displaystyle 4 x^{2} \left(5 x + 9\right) -7 \cdot \left(5 x + 9\right) = \left(5 x + 9\right) \left(4 x^{2} - 7\right)\).

Download \(\LaTeX\) 

\begin{question}Factor $20 x^{3} + 36 x^{2} - 35 x - 63$. 
    \soln{9cm}{Grouping the first two terms and factoring out their GCF, $4 x^{2}$, gives $4 x^{2}(5 x + 9)$. Grouping the last two terms and factoring out their GCF, $-7$, gives $-7(5 x + 9)$. The polynomial now has a common binomial factor of $5 x + 9$. This gives $4 x^{2} \left(5 x + 9\right) -7 \cdot \left(5 x + 9\right) = \left(5 x + 9\right) \left(4 x^{2} - 7\right)$. }

\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} + 36 x^{2} - 35 x - 63 " src="/equation_images/%20%5Cdisplaystyle%2020%20x%5E%7B3%7D%20%2B%2036%20x%5E%7B2%7D%20-%2035%20x%20-%2063%20" alt="LaTeX:  \displaystyle 20 x^{3} + 36 x^{2} - 35 x - 63 " data-equation-content=" \displaystyle 20 x^{3} + 36 x^{2} - 35 x - 63 " /> . </p> </p>
HTML for Canvas
<p> <p>Grouping the first two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle 4 x^{2} " src="/equation_images/%20%5Cdisplaystyle%204%20x%5E%7B2%7D%20" alt="LaTeX:  \displaystyle 4 x^{2} " data-equation-content=" \displaystyle 4 x^{2} " /> , gives  <img class="equation_image" title=" \displaystyle 4 x^{2}(5 x + 9) " src="/equation_images/%20%5Cdisplaystyle%204%20x%5E%7B2%7D%285%20x%20%2B%209%29%20" alt="LaTeX:  \displaystyle 4 x^{2}(5 x + 9) " data-equation-content=" \displaystyle 4 x^{2}(5 x + 9) " /> . Grouping the last two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle -7 " src="/equation_images/%20%5Cdisplaystyle%20-7%20" alt="LaTeX:  \displaystyle -7 " data-equation-content=" \displaystyle -7 " /> , gives  <img class="equation_image" title=" \displaystyle -7(5 x + 9) " src="/equation_images/%20%5Cdisplaystyle%20-7%285%20x%20%2B%209%29%20" alt="LaTeX:  \displaystyle -7(5 x + 9) " data-equation-content=" \displaystyle -7(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%2B%209%20" alt="LaTeX:  \displaystyle 5 x + 9 " data-equation-content=" \displaystyle 5 x + 9 " /> . This gives  <img class="equation_image" title=" \displaystyle 4 x^{2} \left(5 x + 9\right) -7 \cdot \left(5 x + 9\right) = \left(5 x + 9\right) \left(4 x^{2} - 7\right) " src="/equation_images/%20%5Cdisplaystyle%204%20x%5E%7B2%7D%20%5Cleft%285%20x%20%2B%209%5Cright%29%20-7%20%5Ccdot%20%5Cleft%285%20x%20%2B%209%5Cright%29%20%3D%20%5Cleft%285%20x%20%2B%209%5Cright%29%20%5Cleft%284%20x%5E%7B2%7D%20-%207%5Cright%29%20" alt="LaTeX:  \displaystyle 4 x^{2} \left(5 x + 9\right) -7 \cdot \left(5 x + 9\right) = \left(5 x + 9\right) \left(4 x^{2} - 7\right) " data-equation-content=" \displaystyle 4 x^{2} \left(5 x + 9\right) -7 \cdot \left(5 x + 9\right) = \left(5 x + 9\right) \left(4 x^{2} - 7\right) " /> . </p> </p>