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Factor \(\displaystyle - 42 x^{3} + 42 x^{2} - 56 x + 56\).

Factoring out the GCF \(\displaystyle -14\) from each term gives \(\displaystyle -14(3 x^{3} - 3 x^{2} + 4 x - 4)\). Grouping the first two terms and factoring out their GCF, \(\displaystyle 3 x^{2}\), gives \(\displaystyle 3 x^{2}(x - 1)\). Grouping the last two terms and factoring out their GCF, \(\displaystyle 4\), gives \(\displaystyle 4(x - 1)\). The polynomial now has a common binomial factor of \(\displaystyle x - 1\). This gives \(\displaystyle -14[3 x^{2} \left(x - 1\right) +4 \cdot \left(x - 1\right)] = -14\left(x - 1\right) \left(3 x^{2} + 4\right)\).

Download \(\LaTeX\) 

\begin{question}Factor $- 42 x^{3} + 42 x^{2} - 56 x + 56$. 
    \soln{9cm}{Factoring out the GCF $-14$ from each term gives $-14(3 x^{3} - 3 x^{2} + 4 x - 4)$. Grouping the first two terms and factoring out their GCF, $3 x^{2}$, gives $3 x^{2}(x - 1)$. Grouping the last two terms and factoring out their GCF, $4$, gives $4(x - 1)$. The polynomial now has a common binomial factor of $x - 1$. This gives $-14[3 x^{2} \left(x - 1\right) +4 \cdot \left(x - 1\right)] = -14\left(x - 1\right) \left(3 x^{2} + 4\right)$. }

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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HTML for Canvas 
<p> <p>Factor  <img class="equation_image" title=" \displaystyle - 42 x^{3} + 42 x^{2} - 56 x + 56 " src="/equation_images/%20%5Cdisplaystyle%20-%2042%20x%5E%7B3%7D%20%2B%2042%20x%5E%7B2%7D%20-%2056%20x%20%2B%2056%20" alt="LaTeX:  \displaystyle - 42 x^{3} + 42 x^{2} - 56 x + 56 " data-equation-content=" \displaystyle - 42 x^{3} + 42 x^{2} - 56 x + 56 " /> . </p> </p>
HTML for Canvas
<p> <p>Factoring out the GCF  <img class="equation_image" title=" \displaystyle -14 " src="/equation_images/%20%5Cdisplaystyle%20-14%20" alt="LaTeX:  \displaystyle -14 " data-equation-content=" \displaystyle -14 " />  from each term gives  <img class="equation_image" title=" \displaystyle -14(3 x^{3} - 3 x^{2} + 4 x - 4) " src="/equation_images/%20%5Cdisplaystyle%20-14%283%20x%5E%7B3%7D%20-%203%20x%5E%7B2%7D%20%2B%204%20x%20-%204%29%20" alt="LaTeX:  \displaystyle -14(3 x^{3} - 3 x^{2} + 4 x - 4) " data-equation-content=" \displaystyle -14(3 x^{3} - 3 x^{2} + 4 x - 4) " /> . 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 - 1) " src="/equation_images/%20%5Cdisplaystyle%203%20x%5E%7B2%7D%28x%20-%201%29%20" alt="LaTeX:  \displaystyle 3 x^{2}(x - 1) " data-equation-content=" \displaystyle 3 x^{2}(x - 1) " /> . Grouping the last two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle 4 " src="/equation_images/%20%5Cdisplaystyle%204%20" alt="LaTeX:  \displaystyle 4 " data-equation-content=" \displaystyle 4 " /> , gives  <img class="equation_image" title=" \displaystyle 4(x - 1) " src="/equation_images/%20%5Cdisplaystyle%204%28x%20-%201%29%20" alt="LaTeX:  \displaystyle 4(x - 1) " data-equation-content=" \displaystyle 4(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 -14[3 x^{2} \left(x - 1\right) +4 \cdot \left(x - 1\right)] = -14\left(x - 1\right) \left(3 x^{2} + 4\right) " src="/equation_images/%20%5Cdisplaystyle%20-14%5B3%20x%5E%7B2%7D%20%5Cleft%28x%20-%201%5Cright%29%20%2B4%20%5Ccdot%20%5Cleft%28x%20-%201%5Cright%29%5D%20%3D%20-14%5Cleft%28x%20-%201%5Cright%29%20%5Cleft%283%20x%5E%7B2%7D%20%2B%204%5Cright%29%20" alt="LaTeX:  \displaystyle -14[3 x^{2} \left(x - 1\right) +4 \cdot \left(x - 1\right)] = -14\left(x - 1\right) \left(3 x^{2} + 4\right) " data-equation-content=" \displaystyle -14[3 x^{2} \left(x - 1\right) +4 \cdot \left(x - 1\right)] = -14\left(x - 1\right) \left(3 x^{2} + 4\right) " /> . </p> </p>