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Factor \(\displaystyle - 18 x^{3} - 6 x^{2} - 45 x - 15\).

Factoring out the GCF \(\displaystyle -3\) from each term gives \(\displaystyle -3(6 x^{3} + 2 x^{2} + 15 x + 5)\). Grouping the first two terms and factoring out their GCF, \(\displaystyle 2 x^{2}\), gives \(\displaystyle 2 x^{2}(3 x + 1)\). Grouping the last two terms and factoring out their GCF, \(\displaystyle 5\), gives \(\displaystyle 5(3 x + 1)\). The polynomial now has a common binomial factor of \(\displaystyle 3 x + 1\). This gives \(\displaystyle -3[2 x^{2} \left(3 x + 1\right) +5 \cdot \left(3 x + 1\right)] = -3\left(3 x + 1\right) \left(2 x^{2} + 5\right)\).

Download \(\LaTeX\) 

\begin{question}Factor $- 18 x^{3} - 6 x^{2} - 45 x - 15$. 
    \soln{9cm}{Factoring out the GCF $-3$ from each term gives $-3(6 x^{3} + 2 x^{2} + 15 x + 5)$. Grouping the first two terms and factoring out their GCF, $2 x^{2}$, gives $2 x^{2}(3 x + 1)$. Grouping the last two terms and factoring out their GCF, $5$, gives $5(3 x + 1)$. The polynomial now has a common binomial factor of $3 x + 1$. This gives $-3[2 x^{2} \left(3 x + 1\right) +5 \cdot \left(3 x + 1\right)] = -3\left(3 x + 1\right) \left(2 x^{2} + 5\right)$. }

\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} - 6 x^{2} - 45 x - 15 " src="/equation_images/%20%5Cdisplaystyle%20-%2018%20x%5E%7B3%7D%20-%206%20x%5E%7B2%7D%20-%2045%20x%20-%2015%20" alt="LaTeX:  \displaystyle - 18 x^{3} - 6 x^{2} - 45 x - 15 " data-equation-content=" \displaystyle - 18 x^{3} - 6 x^{2} - 45 x - 15 " /> . </p> </p>
HTML for Canvas
<p> <p>Factoring out the GCF  <img class="equation_image" title=" \displaystyle -3 " src="/equation_images/%20%5Cdisplaystyle%20-3%20" alt="LaTeX:  \displaystyle -3 " data-equation-content=" \displaystyle -3 " />  from each term gives  <img class="equation_image" title=" \displaystyle -3(6 x^{3} + 2 x^{2} + 15 x + 5) " src="/equation_images/%20%5Cdisplaystyle%20-3%286%20x%5E%7B3%7D%20%2B%202%20x%5E%7B2%7D%20%2B%2015%20x%20%2B%205%29%20" alt="LaTeX:  \displaystyle -3(6 x^{3} + 2 x^{2} + 15 x + 5) " data-equation-content=" \displaystyle -3(6 x^{3} + 2 x^{2} + 15 x + 5) " /> . 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}(3 x + 1) " src="/equation_images/%20%5Cdisplaystyle%202%20x%5E%7B2%7D%283%20x%20%2B%201%29%20" alt="LaTeX:  \displaystyle 2 x^{2}(3 x + 1) " data-equation-content=" \displaystyle 2 x^{2}(3 x + 1) " /> . Grouping the last two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle 5 " src="/equation_images/%20%5Cdisplaystyle%205%20" alt="LaTeX:  \displaystyle 5 " data-equation-content=" \displaystyle 5 " /> , gives  <img class="equation_image" title=" \displaystyle 5(3 x + 1) " src="/equation_images/%20%5Cdisplaystyle%205%283%20x%20%2B%201%29%20" alt="LaTeX:  \displaystyle 5(3 x + 1) " data-equation-content=" \displaystyle 5(3 x + 1) " /> . The polynomial now has a common binomial factor of  <img class="equation_image" title=" \displaystyle 3 x + 1 " src="/equation_images/%20%5Cdisplaystyle%203%20x%20%2B%201%20" alt="LaTeX:  \displaystyle 3 x + 1 " data-equation-content=" \displaystyle 3 x + 1 " /> . This gives  <img class="equation_image" title=" \displaystyle -3[2 x^{2} \left(3 x + 1\right) +5 \cdot \left(3 x + 1\right)] = -3\left(3 x + 1\right) \left(2 x^{2} + 5\right) " src="/equation_images/%20%5Cdisplaystyle%20-3%5B2%20x%5E%7B2%7D%20%5Cleft%283%20x%20%2B%201%5Cright%29%20%2B5%20%5Ccdot%20%5Cleft%283%20x%20%2B%201%5Cright%29%5D%20%3D%20-3%5Cleft%283%20x%20%2B%201%5Cright%29%20%5Cleft%282%20x%5E%7B2%7D%20%2B%205%5Cright%29%20" alt="LaTeX:  \displaystyle -3[2 x^{2} \left(3 x + 1\right) +5 \cdot \left(3 x + 1\right)] = -3\left(3 x + 1\right) \left(2 x^{2} + 5\right) " data-equation-content=" \displaystyle -3[2 x^{2} \left(3 x + 1\right) +5 \cdot \left(3 x + 1\right)] = -3\left(3 x + 1\right) \left(2 x^{2} + 5\right) " /> . </p> </p>