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Factor \(\displaystyle 60 x^{3} + 80 x^{2} + 18 x + 24\).

Factoring out the GCF \(\displaystyle 2\) from each term gives \(\displaystyle 2(30 x^{3} + 40 x^{2} + 9 x + 12)\). Grouping the first two terms and factoring out their GCF, \(\displaystyle 10 x^{2}\), gives \(\displaystyle 10 x^{2}(3 x + 4)\). Grouping the last two terms and factoring out their GCF, \(\displaystyle 3\), gives \(\displaystyle 3(3 x + 4)\). The polynomial now has a common binomial factor of \(\displaystyle 3 x + 4\). This gives \(\displaystyle 2[10 x^{2} \left(3 x + 4\right) +3 \cdot \left(3 x + 4\right)] = 2\left(3 x + 4\right) \left(10 x^{2} + 3\right)\).

Download \(\LaTeX\) 

\begin{question}Factor $60 x^{3} + 80 x^{2} + 18 x + 24$. 
    \soln{9cm}{Factoring out the GCF $2$ from each term gives $2(30 x^{3} + 40 x^{2} + 9 x + 12)$. Grouping the first two terms and factoring out their GCF, $10 x^{2}$, gives $10 x^{2}(3 x + 4)$. Grouping the last two terms and factoring out their GCF, $3$, gives $3(3 x + 4)$. The polynomial now has a common binomial factor of $3 x + 4$. This gives $2[10 x^{2} \left(3 x + 4\right) +3 \cdot \left(3 x + 4\right)] = 2\left(3 x + 4\right) \left(10 x^{2} + 3\right)$. }

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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HTML for Canvas 
<p> <p>Factor  <img class="equation_image" title=" \displaystyle 60 x^{3} + 80 x^{2} + 18 x + 24 " src="/equation_images/%20%5Cdisplaystyle%2060%20x%5E%7B3%7D%20%2B%2080%20x%5E%7B2%7D%20%2B%2018%20x%20%2B%2024%20" alt="LaTeX:  \displaystyle 60 x^{3} + 80 x^{2} + 18 x + 24 " data-equation-content=" \displaystyle 60 x^{3} + 80 x^{2} + 18 x + 24 " /> . </p> </p>
HTML for Canvas
<p> <p>Factoring out the GCF  <img class="equation_image" title=" \displaystyle 2 " src="/equation_images/%20%5Cdisplaystyle%202%20" alt="LaTeX:  \displaystyle 2 " data-equation-content=" \displaystyle 2 " />  from each term gives  <img class="equation_image" title=" \displaystyle 2(30 x^{3} + 40 x^{2} + 9 x + 12) " src="/equation_images/%20%5Cdisplaystyle%202%2830%20x%5E%7B3%7D%20%2B%2040%20x%5E%7B2%7D%20%2B%209%20x%20%2B%2012%29%20" alt="LaTeX:  \displaystyle 2(30 x^{3} + 40 x^{2} + 9 x + 12) " data-equation-content=" \displaystyle 2(30 x^{3} + 40 x^{2} + 9 x + 12) " /> . Grouping the first two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle 10 x^{2} " src="/equation_images/%20%5Cdisplaystyle%2010%20x%5E%7B2%7D%20" alt="LaTeX:  \displaystyle 10 x^{2} " data-equation-content=" \displaystyle 10 x^{2} " /> , gives  <img class="equation_image" title=" \displaystyle 10 x^{2}(3 x + 4) " src="/equation_images/%20%5Cdisplaystyle%2010%20x%5E%7B2%7D%283%20x%20%2B%204%29%20" alt="LaTeX:  \displaystyle 10 x^{2}(3 x + 4) " data-equation-content=" \displaystyle 10 x^{2}(3 x + 4) " /> . Grouping the last two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle 3 " src="/equation_images/%20%5Cdisplaystyle%203%20" alt="LaTeX:  \displaystyle 3 " data-equation-content=" \displaystyle 3 " /> , gives  <img class="equation_image" title=" \displaystyle 3(3 x + 4) " src="/equation_images/%20%5Cdisplaystyle%203%283%20x%20%2B%204%29%20" alt="LaTeX:  \displaystyle 3(3 x + 4) " data-equation-content=" \displaystyle 3(3 x + 4) " /> . The polynomial now has a common binomial factor of  <img class="equation_image" title=" \displaystyle 3 x + 4 " src="/equation_images/%20%5Cdisplaystyle%203%20x%20%2B%204%20" alt="LaTeX:  \displaystyle 3 x + 4 " data-equation-content=" \displaystyle 3 x + 4 " /> . This gives  <img class="equation_image" title=" \displaystyle 2[10 x^{2} \left(3 x + 4\right) +3 \cdot \left(3 x + 4\right)] = 2\left(3 x + 4\right) \left(10 x^{2} + 3\right) " src="/equation_images/%20%5Cdisplaystyle%202%5B10%20x%5E%7B2%7D%20%5Cleft%283%20x%20%2B%204%5Cright%29%20%2B3%20%5Ccdot%20%5Cleft%283%20x%20%2B%204%5Cright%29%5D%20%3D%202%5Cleft%283%20x%20%2B%204%5Cright%29%20%5Cleft%2810%20x%5E%7B2%7D%20%2B%203%5Cright%29%20" alt="LaTeX:  \displaystyle 2[10 x^{2} \left(3 x + 4\right) +3 \cdot \left(3 x + 4\right)] = 2\left(3 x + 4\right) \left(10 x^{2} + 3\right) " data-equation-content=" \displaystyle 2[10 x^{2} \left(3 x + 4\right) +3 \cdot \left(3 x + 4\right)] = 2\left(3 x + 4\right) \left(10 x^{2} + 3\right) " /> . </p> </p>