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Factor \(\displaystyle - 18 x^{3} - 2 x^{2} - 36 x - 4\).

Factoring out the GCF \(\displaystyle -2\) from each term gives \(\displaystyle -2(9 x^{3} + x^{2} + 18 x + 2)\). Grouping the first two terms and factoring out their GCF, \(\displaystyle x^{2}\), gives \(\displaystyle x^{2}(9 x + 1)\). Grouping the last two terms and factoring out their GCF, \(\displaystyle 2\), gives \(\displaystyle 2(9 x + 1)\). The polynomial now has a common binomial factor of \(\displaystyle 9 x + 1\). This gives \(\displaystyle -2[x^{2} \left(9 x + 1\right) +2 \cdot \left(9 x + 1\right)] = -2\left(9 x + 1\right) \left(x^{2} + 2\right)\).

Download \(\LaTeX\) 

\begin{question}Factor $- 18 x^{3} - 2 x^{2} - 36 x - 4$. 
    \soln{9cm}{Factoring out the GCF $-2$ from each term gives $-2(9 x^{3} + x^{2} + 18 x + 2)$. Grouping the first two terms and factoring out their GCF, $x^{2}$, gives $x^{2}(9 x + 1)$. Grouping the last two terms and factoring out their GCF, $2$, gives $2(9 x + 1)$. The polynomial now has a common binomial factor of $9 x + 1$. This gives $-2[x^{2} \left(9 x + 1\right) +2 \cdot \left(9 x + 1\right)] = -2\left(9 x + 1\right) \left(x^{2} + 2\right)$. }

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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HTML for Canvas 
<p> <p>Factor  <img class="equation_image" title=" \displaystyle - 18 x^{3} - 2 x^{2} - 36 x - 4 " src="/equation_images/%20%5Cdisplaystyle%20-%2018%20x%5E%7B3%7D%20-%202%20x%5E%7B2%7D%20-%2036%20x%20-%204%20" alt="LaTeX:  \displaystyle - 18 x^{3} - 2 x^{2} - 36 x - 4 " data-equation-content=" \displaystyle - 18 x^{3} - 2 x^{2} - 36 x - 4 " /> . </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(9 x^{3} + x^{2} + 18 x + 2) " src="/equation_images/%20%5Cdisplaystyle%20-2%289%20x%5E%7B3%7D%20%2B%20x%5E%7B2%7D%20%2B%2018%20x%20%2B%202%29%20" alt="LaTeX:  \displaystyle -2(9 x^{3} + x^{2} + 18 x + 2) " data-equation-content=" \displaystyle -2(9 x^{3} + x^{2} + 18 x + 2) " /> . Grouping the first two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle x^{2} " src="/equation_images/%20%5Cdisplaystyle%20x%5E%7B2%7D%20" alt="LaTeX:  \displaystyle x^{2} " data-equation-content=" \displaystyle x^{2} " /> , gives  <img class="equation_image" title=" \displaystyle x^{2}(9 x + 1) " src="/equation_images/%20%5Cdisplaystyle%20x%5E%7B2%7D%289%20x%20%2B%201%29%20" alt="LaTeX:  \displaystyle x^{2}(9 x + 1) " data-equation-content=" \displaystyle x^{2}(9 x + 1) " /> . Grouping the last two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle 2 " src="/equation_images/%20%5Cdisplaystyle%202%20" alt="LaTeX:  \displaystyle 2 " data-equation-content=" \displaystyle 2 " /> , gives  <img class="equation_image" title=" \displaystyle 2(9 x + 1) " src="/equation_images/%20%5Cdisplaystyle%202%289%20x%20%2B%201%29%20" alt="LaTeX:  \displaystyle 2(9 x + 1) " data-equation-content=" \displaystyle 2(9 x + 1) " /> . The polynomial now has a common binomial factor of  <img class="equation_image" title=" \displaystyle 9 x + 1 " src="/equation_images/%20%5Cdisplaystyle%209%20x%20%2B%201%20" alt="LaTeX:  \displaystyle 9 x + 1 " data-equation-content=" \displaystyle 9 x + 1 " /> . This gives  <img class="equation_image" title=" \displaystyle -2[x^{2} \left(9 x + 1\right) +2 \cdot \left(9 x + 1\right)] = -2\left(9 x + 1\right) \left(x^{2} + 2\right) " src="/equation_images/%20%5Cdisplaystyle%20-2%5Bx%5E%7B2%7D%20%5Cleft%289%20x%20%2B%201%5Cright%29%20%2B2%20%5Ccdot%20%5Cleft%289%20x%20%2B%201%5Cright%29%5D%20%3D%20-2%5Cleft%289%20x%20%2B%201%5Cright%29%20%5Cleft%28x%5E%7B2%7D%20%2B%202%5Cright%29%20" alt="LaTeX:  \displaystyle -2[x^{2} \left(9 x + 1\right) +2 \cdot \left(9 x + 1\right)] = -2\left(9 x + 1\right) \left(x^{2} + 2\right) " data-equation-content=" \displaystyle -2[x^{2} \left(9 x + 1\right) +2 \cdot \left(9 x + 1\right)] = -2\left(9 x + 1\right) \left(x^{2} + 2\right) " /> . </p> </p>