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Factor \(\displaystyle - 6 x^{3} + 6 x^{2} + 7 x - 7\).

Factoring out the GCF \(\displaystyle -1\) from each term gives \(\displaystyle -(6 x^{3} - 6 x^{2} - 7 x + 7)\). Grouping the first two terms and factoring out their GCF, \(\displaystyle 6 x^{2}\), gives \(\displaystyle 6 x^{2}(x - 1)\). Grouping the last two terms and factoring out their GCF, \(\displaystyle -7\), gives \(\displaystyle -7(x - 1)\). The polynomial now has a common binomial factor of \(\displaystyle x - 1\). This gives \(\displaystyle -1[6 x^{2} \left(x - 1\right) -7 \cdot \left(x - 1\right)] = -\left(x - 1\right) \left(6 x^{2} - 7\right)\).

Download \(\LaTeX\) 

\begin{question}Factor $- 6 x^{3} + 6 x^{2} + 7 x - 7$. 
    \soln{9cm}{Factoring out the GCF $-1$ from each term gives $-(6 x^{3} - 6 x^{2} - 7 x + 7)$. Grouping the first two terms and factoring out their GCF, $6 x^{2}$, gives $6 x^{2}(x - 1)$. Grouping the last two terms and factoring out their GCF, $-7$, gives $-7(x - 1)$. The polynomial now has a common binomial factor of $x - 1$. This gives $-1[6 x^{2} \left(x - 1\right) -7 \cdot \left(x - 1\right)] = -\left(x - 1\right) \left(6 x^{2} - 7\right)$. }

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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HTML for Canvas 
<p> <p>Factor  <img class="equation_image" title=" \displaystyle - 6 x^{3} + 6 x^{2} + 7 x - 7 " src="/equation_images/%20%5Cdisplaystyle%20-%206%20x%5E%7B3%7D%20%2B%206%20x%5E%7B2%7D%20%2B%207%20x%20-%207%20" alt="LaTeX:  \displaystyle - 6 x^{3} + 6 x^{2} + 7 x - 7 " data-equation-content=" \displaystyle - 6 x^{3} + 6 x^{2} + 7 x - 7 " /> . </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 -(6 x^{3} - 6 x^{2} - 7 x + 7) " src="/equation_images/%20%5Cdisplaystyle%20-%286%20x%5E%7B3%7D%20-%206%20x%5E%7B2%7D%20-%207%20x%20%2B%207%29%20" alt="LaTeX:  \displaystyle -(6 x^{3} - 6 x^{2} - 7 x + 7) " data-equation-content=" \displaystyle -(6 x^{3} - 6 x^{2} - 7 x + 7) " /> . Grouping the first two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle 6 x^{2} " src="/equation_images/%20%5Cdisplaystyle%206%20x%5E%7B2%7D%20" alt="LaTeX:  \displaystyle 6 x^{2} " data-equation-content=" \displaystyle 6 x^{2} " /> , gives  <img class="equation_image" title=" \displaystyle 6 x^{2}(x - 1) " src="/equation_images/%20%5Cdisplaystyle%206%20x%5E%7B2%7D%28x%20-%201%29%20" alt="LaTeX:  \displaystyle 6 x^{2}(x - 1) " data-equation-content=" \displaystyle 6 x^{2}(x - 1) " /> . Grouping the last two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle -7 " src="/equation_images/%20%5Cdisplaystyle%20-7%20" alt="LaTeX:  \displaystyle -7 " data-equation-content=" \displaystyle -7 " /> , gives  <img class="equation_image" title=" \displaystyle -7(x - 1) " src="/equation_images/%20%5Cdisplaystyle%20-7%28x%20-%201%29%20" alt="LaTeX:  \displaystyle -7(x - 1) " data-equation-content=" \displaystyle -7(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 -1[6 x^{2} \left(x - 1\right) -7 \cdot \left(x - 1\right)] = -\left(x - 1\right) \left(6 x^{2} - 7\right) " src="/equation_images/%20%5Cdisplaystyle%20-1%5B6%20x%5E%7B2%7D%20%5Cleft%28x%20-%201%5Cright%29%20-7%20%5Ccdot%20%5Cleft%28x%20-%201%5Cright%29%5D%20%3D%20-%5Cleft%28x%20-%201%5Cright%29%20%5Cleft%286%20x%5E%7B2%7D%20-%207%5Cright%29%20" alt="LaTeX:  \displaystyle -1[6 x^{2} \left(x - 1\right) -7 \cdot \left(x - 1\right)] = -\left(x - 1\right) \left(6 x^{2} - 7\right) " data-equation-content=" \displaystyle -1[6 x^{2} \left(x - 1\right) -7 \cdot \left(x - 1\right)] = -\left(x - 1\right) \left(6 x^{2} - 7\right) " /> . </p> </p>