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

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

Download \(\LaTeX\) 

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

\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} - 50 x^{2} + 15 x - 15 " src="/equation_images/%20%5Cdisplaystyle%2050%20x%5E%7B3%7D%20-%2050%20x%5E%7B2%7D%20%2B%2015%20x%20-%2015%20" alt="LaTeX:  \displaystyle 50 x^{3} - 50 x^{2} + 15 x - 15 " data-equation-content=" \displaystyle 50 x^{3} - 50 x^{2} + 15 x - 15 " /> . </p> </p>
HTML for Canvas
<p> <p>Factoring out the GCF  <img class="equation_image" title=" \displaystyle 5 " src="/equation_images/%20%5Cdisplaystyle%205%20" alt="LaTeX:  \displaystyle 5 " data-equation-content=" \displaystyle 5 " />  from each term gives  <img class="equation_image" title=" \displaystyle 5(10 x^{3} - 10 x^{2} + 3 x - 3) " src="/equation_images/%20%5Cdisplaystyle%205%2810%20x%5E%7B3%7D%20-%2010%20x%5E%7B2%7D%20%2B%203%20x%20-%203%29%20" alt="LaTeX:  \displaystyle 5(10 x^{3} - 10 x^{2} + 3 x - 3) " data-equation-content=" \displaystyle 5(10 x^{3} - 10 x^{2} + 3 x - 3) " /> . Grouping the first two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle 10 x^{2} " src="/equation_images/%20%5Cdisplaystyle%2010%20x%5E%7B2%7D%20" alt="LaTeX:  \displaystyle 10 x^{2} " data-equation-content=" \displaystyle 10 x^{2} " /> , gives  <img class="equation_image" title=" \displaystyle 10 x^{2}(x - 1) " src="/equation_images/%20%5Cdisplaystyle%2010%20x%5E%7B2%7D%28x%20-%201%29%20" alt="LaTeX:  \displaystyle 10 x^{2}(x - 1) " data-equation-content=" \displaystyle 10 x^{2}(x - 1) " /> . Grouping the last two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle 3 " src="/equation_images/%20%5Cdisplaystyle%203%20" alt="LaTeX:  \displaystyle 3 " data-equation-content=" \displaystyle 3 " /> , gives  <img class="equation_image" title=" \displaystyle 3(x - 1) " src="/equation_images/%20%5Cdisplaystyle%203%28x%20-%201%29%20" alt="LaTeX:  \displaystyle 3(x - 1) " data-equation-content=" \displaystyle 3(x - 1) " /> . The polynomial now has a common binomial factor of  <img class="equation_image" title=" \displaystyle x - 1 " src="/equation_images/%20%5Cdisplaystyle%20x%20-%201%20" alt="LaTeX:  \displaystyle x - 1 " data-equation-content=" \displaystyle x - 1 " /> . This gives  <img class="equation_image" title=" \displaystyle 5[10 x^{2} \left(x - 1\right) +3 \cdot \left(x - 1\right)] = 5\left(x - 1\right) \left(10 x^{2} + 3\right) " src="/equation_images/%20%5Cdisplaystyle%205%5B10%20x%5E%7B2%7D%20%5Cleft%28x%20-%201%5Cright%29%20%2B3%20%5Ccdot%20%5Cleft%28x%20-%201%5Cright%29%5D%20%3D%205%5Cleft%28x%20-%201%5Cright%29%20%5Cleft%2810%20x%5E%7B2%7D%20%2B%203%5Cright%29%20" alt="LaTeX:  \displaystyle 5[10 x^{2} \left(x - 1\right) +3 \cdot \left(x - 1\right)] = 5\left(x - 1\right) \left(10 x^{2} + 3\right) " data-equation-content=" \displaystyle 5[10 x^{2} \left(x - 1\right) +3 \cdot \left(x - 1\right)] = 5\left(x - 1\right) \left(10 x^{2} + 3\right) " /> . </p> </p>