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Factor \(\displaystyle - 21 x^{3} - 30 x^{2} + 35 x + 50\).

Factoring out the GCF \(\displaystyle -1\) from each term gives \(\displaystyle -(21 x^{3} + 30 x^{2} - 35 x - 50)\). Grouping the first two terms and factoring out their GCF, \(\displaystyle 3 x^{2}\), gives \(\displaystyle 3 x^{2}(7 x + 10)\). Grouping the last two terms and factoring out their GCF, \(\displaystyle -5\), gives \(\displaystyle -5(7 x + 10)\). The polynomial now has a common binomial factor of \(\displaystyle 7 x + 10\). This gives \(\displaystyle -1[3 x^{2} \left(7 x + 10\right) -5 \cdot \left(7 x + 10\right)] = -\left(7 x + 10\right) \left(3 x^{2} - 5\right)\).

Download \(\LaTeX\) 

\begin{question}Factor $- 21 x^{3} - 30 x^{2} + 35 x + 50$. 
    \soln{9cm}{Factoring out the GCF $-1$ from each term gives $-(21 x^{3} + 30 x^{2} - 35 x - 50)$. Grouping the first two terms and factoring out their GCF, $3 x^{2}$, gives $3 x^{2}(7 x + 10)$. Grouping the last two terms and factoring out their GCF, $-5$, gives $-5(7 x + 10)$. The polynomial now has a common binomial factor of $7 x + 10$. This gives $-1[3 x^{2} \left(7 x + 10\right) -5 \cdot \left(7 x + 10\right)] = -\left(7 x + 10\right) \left(3 x^{2} - 5\right)$. }

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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HTML for Canvas 
<p> <p>Factor  <img class="equation_image" title=" \displaystyle - 21 x^{3} - 30 x^{2} + 35 x + 50 " src="/equation_images/%20%5Cdisplaystyle%20-%2021%20x%5E%7B3%7D%20-%2030%20x%5E%7B2%7D%20%2B%2035%20x%20%2B%2050%20" alt="LaTeX:  \displaystyle - 21 x^{3} - 30 x^{2} + 35 x + 50 " data-equation-content=" \displaystyle - 21 x^{3} - 30 x^{2} + 35 x + 50 " /> . </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 -(21 x^{3} + 30 x^{2} - 35 x - 50) " src="/equation_images/%20%5Cdisplaystyle%20-%2821%20x%5E%7B3%7D%20%2B%2030%20x%5E%7B2%7D%20-%2035%20x%20-%2050%29%20" alt="LaTeX:  \displaystyle -(21 x^{3} + 30 x^{2} - 35 x - 50) " data-equation-content=" \displaystyle -(21 x^{3} + 30 x^{2} - 35 x - 50) " /> . 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}(7 x + 10) " src="/equation_images/%20%5Cdisplaystyle%203%20x%5E%7B2%7D%287%20x%20%2B%2010%29%20" alt="LaTeX:  \displaystyle 3 x^{2}(7 x + 10) " data-equation-content=" \displaystyle 3 x^{2}(7 x + 10) " /> . Grouping the last two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle -5 " src="/equation_images/%20%5Cdisplaystyle%20-5%20" alt="LaTeX:  \displaystyle -5 " data-equation-content=" \displaystyle -5 " /> , gives  <img class="equation_image" title=" \displaystyle -5(7 x + 10) " src="/equation_images/%20%5Cdisplaystyle%20-5%287%20x%20%2B%2010%29%20" alt="LaTeX:  \displaystyle -5(7 x + 10) " data-equation-content=" \displaystyle -5(7 x + 10) " /> . The polynomial now has a common binomial factor of  <img class="equation_image" title=" \displaystyle 7 x + 10 " src="/equation_images/%20%5Cdisplaystyle%207%20x%20%2B%2010%20" alt="LaTeX:  \displaystyle 7 x + 10 " data-equation-content=" \displaystyle 7 x + 10 " /> . This gives  <img class="equation_image" title=" \displaystyle -1[3 x^{2} \left(7 x + 10\right) -5 \cdot \left(7 x + 10\right)] = -\left(7 x + 10\right) \left(3 x^{2} - 5\right) " src="/equation_images/%20%5Cdisplaystyle%20-1%5B3%20x%5E%7B2%7D%20%5Cleft%287%20x%20%2B%2010%5Cright%29%20-5%20%5Ccdot%20%5Cleft%287%20x%20%2B%2010%5Cright%29%5D%20%3D%20-%5Cleft%287%20x%20%2B%2010%5Cright%29%20%5Cleft%283%20x%5E%7B2%7D%20-%205%5Cright%29%20" alt="LaTeX:  \displaystyle -1[3 x^{2} \left(7 x + 10\right) -5 \cdot \left(7 x + 10\right)] = -\left(7 x + 10\right) \left(3 x^{2} - 5\right) " data-equation-content=" \displaystyle -1[3 x^{2} \left(7 x + 10\right) -5 \cdot \left(7 x + 10\right)] = -\left(7 x + 10\right) \left(3 x^{2} - 5\right) " /> . </p> </p>