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Factor \(\displaystyle - 15 x^{3} + 18 x^{2} - 40 x + 48\).

Factoring out the GCF \(\displaystyle -1\) from each term gives \(\displaystyle -(15 x^{3} - 18 x^{2} + 40 x - 48)\). Grouping the first two terms and factoring out their GCF, \(\displaystyle 3 x^{2}\), gives \(\displaystyle 3 x^{2}(5 x - 6)\). Grouping the last two terms and factoring out their GCF, \(\displaystyle 8\), gives \(\displaystyle 8(5 x - 6)\). The polynomial now has a common binomial factor of \(\displaystyle 5 x - 6\). This gives \(\displaystyle -1[3 x^{2} \left(5 x - 6\right) +8 \cdot \left(5 x - 6\right)] = -\left(5 x - 6\right) \left(3 x^{2} + 8\right)\).

Download \(\LaTeX\) 

\begin{question}Factor $- 15 x^{3} + 18 x^{2} - 40 x + 48$. 
    \soln{9cm}{Factoring out the GCF $-1$ from each term gives $-(15 x^{3} - 18 x^{2} + 40 x - 48)$. Grouping the first two terms and factoring out their GCF, $3 x^{2}$, gives $3 x^{2}(5 x - 6)$. Grouping the last two terms and factoring out their GCF, $8$, gives $8(5 x - 6)$. The polynomial now has a common binomial factor of $5 x - 6$. This gives $-1[3 x^{2} \left(5 x - 6\right) +8 \cdot \left(5 x - 6\right)] = -\left(5 x - 6\right) \left(3 x^{2} + 8\right)$. }

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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HTML for Canvas 
<p> <p>Factor  <img class="equation_image" title=" \displaystyle - 15 x^{3} + 18 x^{2} - 40 x + 48 " src="/equation_images/%20%5Cdisplaystyle%20-%2015%20x%5E%7B3%7D%20%2B%2018%20x%5E%7B2%7D%20-%2040%20x%20%2B%2048%20" alt="LaTeX:  \displaystyle - 15 x^{3} + 18 x^{2} - 40 x + 48 " data-equation-content=" \displaystyle - 15 x^{3} + 18 x^{2} - 40 x + 48 " /> . </p> </p>
HTML for Canvas
<p> <p>Factoring out the GCF  <img class="equation_image" title=" \displaystyle -1 " src="/equation_images/%20%5Cdisplaystyle%20-1%20" alt="LaTeX:  \displaystyle -1 " data-equation-content=" \displaystyle -1 " />  from each term gives  <img class="equation_image" title=" \displaystyle -(15 x^{3} - 18 x^{2} + 40 x - 48) " src="/equation_images/%20%5Cdisplaystyle%20-%2815%20x%5E%7B3%7D%20-%2018%20x%5E%7B2%7D%20%2B%2040%20x%20-%2048%29%20" alt="LaTeX:  \displaystyle -(15 x^{3} - 18 x^{2} + 40 x - 48) " data-equation-content=" \displaystyle -(15 x^{3} - 18 x^{2} + 40 x - 48) " /> . Grouping the first two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle 3 x^{2} " src="/equation_images/%20%5Cdisplaystyle%203%20x%5E%7B2%7D%20" alt="LaTeX:  \displaystyle 3 x^{2} " data-equation-content=" \displaystyle 3 x^{2} " /> , gives  <img class="equation_image" title=" \displaystyle 3 x^{2}(5 x - 6) " src="/equation_images/%20%5Cdisplaystyle%203%20x%5E%7B2%7D%285%20x%20-%206%29%20" alt="LaTeX:  \displaystyle 3 x^{2}(5 x - 6) " data-equation-content=" \displaystyle 3 x^{2}(5 x - 6) " /> . Grouping the last two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle 8 " src="/equation_images/%20%5Cdisplaystyle%208%20" alt="LaTeX:  \displaystyle 8 " data-equation-content=" \displaystyle 8 " /> , gives  <img class="equation_image" title=" \displaystyle 8(5 x - 6) " src="/equation_images/%20%5Cdisplaystyle%208%285%20x%20-%206%29%20" alt="LaTeX:  \displaystyle 8(5 x - 6) " data-equation-content=" \displaystyle 8(5 x - 6) " /> . The polynomial now has a common binomial factor of  <img class="equation_image" title=" \displaystyle 5 x - 6 " src="/equation_images/%20%5Cdisplaystyle%205%20x%20-%206%20" alt="LaTeX:  \displaystyle 5 x - 6 " data-equation-content=" \displaystyle 5 x - 6 " /> . This gives  <img class="equation_image" title=" \displaystyle -1[3 x^{2} \left(5 x - 6\right) +8 \cdot \left(5 x - 6\right)] = -\left(5 x - 6\right) \left(3 x^{2} + 8\right) " src="/equation_images/%20%5Cdisplaystyle%20-1%5B3%20x%5E%7B2%7D%20%5Cleft%285%20x%20-%206%5Cright%29%20%2B8%20%5Ccdot%20%5Cleft%285%20x%20-%206%5Cright%29%5D%20%3D%20-%5Cleft%285%20x%20-%206%5Cright%29%20%5Cleft%283%20x%5E%7B2%7D%20%2B%208%5Cright%29%20" alt="LaTeX:  \displaystyle -1[3 x^{2} \left(5 x - 6\right) +8 \cdot \left(5 x - 6\right)] = -\left(5 x - 6\right) \left(3 x^{2} + 8\right) " data-equation-content=" \displaystyle -1[3 x^{2} \left(5 x - 6\right) +8 \cdot \left(5 x - 6\right)] = -\left(5 x - 6\right) \left(3 x^{2} + 8\right) " /> . </p> </p>