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Factor \(\displaystyle 3 x^{3} - 21 x^{2} - 10 x + 70\).

Grouping the first two terms and factoring out their GCF, \(\displaystyle 3 x^{2}\), gives \(\displaystyle 3 x^{2}(x - 7)\). Grouping the last two terms and factoring out their GCF, \(\displaystyle -10\), gives \(\displaystyle -10(x - 7)\). The polynomial now has a common binomial factor of \(\displaystyle x - 7\). This gives \(\displaystyle 3 x^{2} \left(x - 7\right) -10 \cdot \left(x - 7\right) = \left(x - 7\right) \left(3 x^{2} - 10\right)\).

Download \(\LaTeX\) 

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

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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    \soln{9cm}{The solution goes here.}

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HTML for Canvas 
<p> <p>Factor  <img class="equation_image" title=" \displaystyle 3 x^{3} - 21 x^{2} - 10 x + 70 " src="/equation_images/%20%5Cdisplaystyle%203%20x%5E%7B3%7D%20-%2021%20x%5E%7B2%7D%20-%2010%20x%20%2B%2070%20" alt="LaTeX:  \displaystyle 3 x^{3} - 21 x^{2} - 10 x + 70 " data-equation-content=" \displaystyle 3 x^{3} - 21 x^{2} - 10 x + 70 " /> . </p> </p>
HTML for Canvas
<p> <p>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}(x - 7) " src="/equation_images/%20%5Cdisplaystyle%203%20x%5E%7B2%7D%28x%20-%207%29%20" alt="LaTeX:  \displaystyle 3 x^{2}(x - 7) " data-equation-content=" \displaystyle 3 x^{2}(x - 7) " /> . Grouping the last two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle -10 " src="/equation_images/%20%5Cdisplaystyle%20-10%20" alt="LaTeX:  \displaystyle -10 " data-equation-content=" \displaystyle -10 " /> , gives  <img class="equation_image" title=" \displaystyle -10(x - 7) " src="/equation_images/%20%5Cdisplaystyle%20-10%28x%20-%207%29%20" alt="LaTeX:  \displaystyle -10(x - 7) " data-equation-content=" \displaystyle -10(x - 7) " /> . The polynomial now has a common binomial factor of  <img class="equation_image" title=" \displaystyle x - 7 " src="/equation_images/%20%5Cdisplaystyle%20x%20-%207%20" alt="LaTeX:  \displaystyle x - 7 " data-equation-content=" \displaystyle x - 7 " /> . This gives  <img class="equation_image" title=" \displaystyle 3 x^{2} \left(x - 7\right) -10 \cdot \left(x - 7\right) = \left(x - 7\right) \left(3 x^{2} - 10\right) " src="/equation_images/%20%5Cdisplaystyle%203%20x%5E%7B2%7D%20%5Cleft%28x%20-%207%5Cright%29%20-10%20%5Ccdot%20%5Cleft%28x%20-%207%5Cright%29%20%3D%20%5Cleft%28x%20-%207%5Cright%29%20%5Cleft%283%20x%5E%7B2%7D%20-%2010%5Cright%29%20" alt="LaTeX:  \displaystyle 3 x^{2} \left(x - 7\right) -10 \cdot \left(x - 7\right) = \left(x - 7\right) \left(3 x^{2} - 10\right) " data-equation-content=" \displaystyle 3 x^{2} \left(x - 7\right) -10 \cdot \left(x - 7\right) = \left(x - 7\right) \left(3 x^{2} - 10\right) " /> . </p> </p>