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Factor \(\displaystyle 90 x^{3} + 60 x^{2} - 36 x - 24\).

Factoring out the GCF \(\displaystyle 6\) from each term gives \(\displaystyle 6(15 x^{3} + 10 x^{2} - 6 x - 4)\). Grouping the first two terms and factoring out their GCF, \(\displaystyle 5 x^{2}\), gives \(\displaystyle 5 x^{2}(3 x + 2)\). Grouping the last two terms and factoring out their GCF, \(\displaystyle -2\), gives \(\displaystyle -2(3 x + 2)\). The polynomial now has a common binomial factor of \(\displaystyle 3 x + 2\). This gives \(\displaystyle 6[5 x^{2} \left(3 x + 2\right) -2 \cdot \left(3 x + 2\right)] = 6\left(3 x + 2\right) \left(5 x^{2} - 2\right)\).

Download \(\LaTeX\) 

\begin{question}Factor $90 x^{3} + 60 x^{2} - 36 x - 24$. 
    \soln{9cm}{Factoring out the GCF $6$ from each term gives $6(15 x^{3} + 10 x^{2} - 6 x - 4)$. Grouping the first two terms and factoring out their GCF, $5 x^{2}$, gives $5 x^{2}(3 x + 2)$. Grouping the last two terms and factoring out their GCF, $-2$, gives $-2(3 x + 2)$. The polynomial now has a common binomial factor of $3 x + 2$. This gives $6[5 x^{2} \left(3 x + 2\right) -2 \cdot \left(3 x + 2\right)] = 6\left(3 x + 2\right) \left(5 x^{2} - 2\right)$. }

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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HTML for Canvas 
<p> <p>Factor  <img class="equation_image" title=" \displaystyle 90 x^{3} + 60 x^{2} - 36 x - 24 " src="/equation_images/%20%5Cdisplaystyle%2090%20x%5E%7B3%7D%20%2B%2060%20x%5E%7B2%7D%20-%2036%20x%20-%2024%20" alt="LaTeX:  \displaystyle 90 x^{3} + 60 x^{2} - 36 x - 24 " data-equation-content=" \displaystyle 90 x^{3} + 60 x^{2} - 36 x - 24 " /> . </p> </p>
HTML for Canvas
<p> <p>Factoring out the GCF  <img class="equation_image" title=" \displaystyle 6 " src="/equation_images/%20%5Cdisplaystyle%206%20" alt="LaTeX:  \displaystyle 6 " data-equation-content=" \displaystyle 6 " />  from each term gives  <img class="equation_image" title=" \displaystyle 6(15 x^{3} + 10 x^{2} - 6 x - 4) " src="/equation_images/%20%5Cdisplaystyle%206%2815%20x%5E%7B3%7D%20%2B%2010%20x%5E%7B2%7D%20-%206%20x%20-%204%29%20" alt="LaTeX:  \displaystyle 6(15 x^{3} + 10 x^{2} - 6 x - 4) " data-equation-content=" \displaystyle 6(15 x^{3} + 10 x^{2} - 6 x - 4) " /> . 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}(3 x + 2) " src="/equation_images/%20%5Cdisplaystyle%205%20x%5E%7B2%7D%283%20x%20%2B%202%29%20" alt="LaTeX:  \displaystyle 5 x^{2}(3 x + 2) " data-equation-content=" \displaystyle 5 x^{2}(3 x + 2) " /> . Grouping the last two terms and factoring out their 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 " /> , gives  <img class="equation_image" title=" \displaystyle -2(3 x + 2) " src="/equation_images/%20%5Cdisplaystyle%20-2%283%20x%20%2B%202%29%20" alt="LaTeX:  \displaystyle -2(3 x + 2) " data-equation-content=" \displaystyle -2(3 x + 2) " /> . The polynomial now has a common binomial factor of  <img class="equation_image" title=" \displaystyle 3 x + 2 " src="/equation_images/%20%5Cdisplaystyle%203%20x%20%2B%202%20" alt="LaTeX:  \displaystyle 3 x + 2 " data-equation-content=" \displaystyle 3 x + 2 " /> . This gives  <img class="equation_image" title=" \displaystyle 6[5 x^{2} \left(3 x + 2\right) -2 \cdot \left(3 x + 2\right)] = 6\left(3 x + 2\right) \left(5 x^{2} - 2\right) " src="/equation_images/%20%5Cdisplaystyle%206%5B5%20x%5E%7B2%7D%20%5Cleft%283%20x%20%2B%202%5Cright%29%20-2%20%5Ccdot%20%5Cleft%283%20x%20%2B%202%5Cright%29%5D%20%3D%206%5Cleft%283%20x%20%2B%202%5Cright%29%20%5Cleft%285%20x%5E%7B2%7D%20-%202%5Cright%29%20" alt="LaTeX:  \displaystyle 6[5 x^{2} \left(3 x + 2\right) -2 \cdot \left(3 x + 2\right)] = 6\left(3 x + 2\right) \left(5 x^{2} - 2\right) " data-equation-content=" \displaystyle 6[5 x^{2} \left(3 x + 2\right) -2 \cdot \left(3 x + 2\right)] = 6\left(3 x + 2\right) \left(5 x^{2} - 2\right) " /> . </p> </p>