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Factor \(\displaystyle - 50 x^{3} + 15 x^{2} - 70 x + 21\).

Factoring out the GCF \(\displaystyle -1\) from each term gives \(\displaystyle -(50 x^{3} - 15 x^{2} + 70 x - 21)\). Grouping the first two terms and factoring out their GCF, \(\displaystyle 5 x^{2}\), gives \(\displaystyle 5 x^{2}(10 x - 3)\). Grouping the last two terms and factoring out their GCF, \(\displaystyle 7\), gives \(\displaystyle 7(10 x - 3)\). The polynomial now has a common binomial factor of \(\displaystyle 10 x - 3\). This gives \(\displaystyle -1[5 x^{2} \left(10 x - 3\right) +7 \cdot \left(10 x - 3\right)] = -\left(10 x - 3\right) \left(5 x^{2} + 7\right)\).

Download \(\LaTeX\) 

\begin{question}Factor $- 50 x^{3} + 15 x^{2} - 70 x + 21$. 
    \soln{9cm}{Factoring out the GCF $-1$ from each term gives $-(50 x^{3} - 15 x^{2} + 70 x - 21)$. Grouping the first two terms and factoring out their GCF, $5 x^{2}$, gives $5 x^{2}(10 x - 3)$. Grouping the last two terms and factoring out their GCF, $7$, gives $7(10 x - 3)$. The polynomial now has a common binomial factor of $10 x - 3$. This gives $-1[5 x^{2} \left(10 x - 3\right) +7 \cdot \left(10 x - 3\right)] = -\left(10 x - 3\right) \left(5 x^{2} + 7\right)$. }

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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HTML for Canvas 
<p> <p>Factor  <img class="equation_image" title=" \displaystyle - 50 x^{3} + 15 x^{2} - 70 x + 21 " src="/equation_images/%20%5Cdisplaystyle%20-%2050%20x%5E%7B3%7D%20%2B%2015%20x%5E%7B2%7D%20-%2070%20x%20%2B%2021%20" alt="LaTeX:  \displaystyle - 50 x^{3} + 15 x^{2} - 70 x + 21 " data-equation-content=" \displaystyle - 50 x^{3} + 15 x^{2} - 70 x + 21 " /> . </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 -(50 x^{3} - 15 x^{2} + 70 x - 21) " src="/equation_images/%20%5Cdisplaystyle%20-%2850%20x%5E%7B3%7D%20-%2015%20x%5E%7B2%7D%20%2B%2070%20x%20-%2021%29%20" alt="LaTeX:  \displaystyle -(50 x^{3} - 15 x^{2} + 70 x - 21) " data-equation-content=" \displaystyle -(50 x^{3} - 15 x^{2} + 70 x - 21) " /> . 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}(10 x - 3) " src="/equation_images/%20%5Cdisplaystyle%205%20x%5E%7B2%7D%2810%20x%20-%203%29%20" alt="LaTeX:  \displaystyle 5 x^{2}(10 x - 3) " data-equation-content=" \displaystyle 5 x^{2}(10 x - 3) " /> . Grouping the last two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle 7 " src="/equation_images/%20%5Cdisplaystyle%207%20" alt="LaTeX:  \displaystyle 7 " data-equation-content=" \displaystyle 7 " /> , gives  <img class="equation_image" title=" \displaystyle 7(10 x - 3) " src="/equation_images/%20%5Cdisplaystyle%207%2810%20x%20-%203%29%20" alt="LaTeX:  \displaystyle 7(10 x - 3) " data-equation-content=" \displaystyle 7(10 x - 3) " /> . The polynomial now has a common binomial factor of  <img class="equation_image" title=" \displaystyle 10 x - 3 " src="/equation_images/%20%5Cdisplaystyle%2010%20x%20-%203%20" alt="LaTeX:  \displaystyle 10 x - 3 " data-equation-content=" \displaystyle 10 x - 3 " /> . This gives  <img class="equation_image" title=" \displaystyle -1[5 x^{2} \left(10 x - 3\right) +7 \cdot \left(10 x - 3\right)] = -\left(10 x - 3\right) \left(5 x^{2} + 7\right) " src="/equation_images/%20%5Cdisplaystyle%20-1%5B5%20x%5E%7B2%7D%20%5Cleft%2810%20x%20-%203%5Cright%29%20%2B7%20%5Ccdot%20%5Cleft%2810%20x%20-%203%5Cright%29%5D%20%3D%20-%5Cleft%2810%20x%20-%203%5Cright%29%20%5Cleft%285%20x%5E%7B2%7D%20%2B%207%5Cright%29%20" alt="LaTeX:  \displaystyle -1[5 x^{2} \left(10 x - 3\right) +7 \cdot \left(10 x - 3\right)] = -\left(10 x - 3\right) \left(5 x^{2} + 7\right) " data-equation-content=" \displaystyle -1[5 x^{2} \left(10 x - 3\right) +7 \cdot \left(10 x - 3\right)] = -\left(10 x - 3\right) \left(5 x^{2} + 7\right) " /> . </p> </p>