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Questions: Algebra BusinessCalculus

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Factor \(\displaystyle 14 x^{3} - 12 x^{2} + 7 x - 6\).

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

Download \(\LaTeX\) 

\begin{question}Factor $14 x^{3} - 12 x^{2} + 7 x - 6$. 
    \soln{9cm}{Grouping the first two terms and factoring out their GCF, $2 x^{2}$, gives $2 x^{2}(7 x - 6)$. Grouping the last two terms and factoring out their GCF, $1$, gives $1(7 x - 6)$. The polynomial now has a common binomial factor of $7 x - 6$. This gives $2 x^{2} \left(7 x - 6\right) +1 \cdot \left(7 x - 6\right) = \left(7 x - 6\right) \left(2 x^{2} + 1\right)$. }

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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HTML for Canvas 
<p> <p>Factor  <img class="equation_image" title=" \displaystyle 14 x^{3} - 12 x^{2} + 7 x - 6 " src="/equation_images/%20%5Cdisplaystyle%2014%20x%5E%7B3%7D%20-%2012%20x%5E%7B2%7D%20%2B%207%20x%20-%206%20" alt="LaTeX:  \displaystyle 14 x^{3} - 12 x^{2} + 7 x - 6 " data-equation-content=" \displaystyle 14 x^{3} - 12 x^{2} + 7 x - 6 " /> . </p> </p>
HTML for Canvas
<p> <p>Grouping the first two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle 2 x^{2} " src="/equation_images/%20%5Cdisplaystyle%202%20x%5E%7B2%7D%20" alt="LaTeX:  \displaystyle 2 x^{2} " data-equation-content=" \displaystyle 2 x^{2} " /> , gives  <img class="equation_image" title=" \displaystyle 2 x^{2}(7 x - 6) " src="/equation_images/%20%5Cdisplaystyle%202%20x%5E%7B2%7D%287%20x%20-%206%29%20" alt="LaTeX:  \displaystyle 2 x^{2}(7 x - 6) " data-equation-content=" \displaystyle 2 x^{2}(7 x - 6) " /> . Grouping the last two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle 1 " src="/equation_images/%20%5Cdisplaystyle%201%20" alt="LaTeX:  \displaystyle 1 " data-equation-content=" \displaystyle 1 " /> , gives  <img class="equation_image" title=" \displaystyle 1(7 x - 6) " src="/equation_images/%20%5Cdisplaystyle%201%287%20x%20-%206%29%20" alt="LaTeX:  \displaystyle 1(7 x - 6) " data-equation-content=" \displaystyle 1(7 x - 6) " /> . The polynomial now has a common binomial factor of  <img class="equation_image" title=" \displaystyle 7 x - 6 " src="/equation_images/%20%5Cdisplaystyle%207%20x%20-%206%20" alt="LaTeX:  \displaystyle 7 x - 6 " data-equation-content=" \displaystyle 7 x - 6 " /> . This gives  <img class="equation_image" title=" \displaystyle 2 x^{2} \left(7 x - 6\right) +1 \cdot \left(7 x - 6\right) = \left(7 x - 6\right) \left(2 x^{2} + 1\right) " src="/equation_images/%20%5Cdisplaystyle%202%20x%5E%7B2%7D%20%5Cleft%287%20x%20-%206%5Cright%29%20%2B1%20%5Ccdot%20%5Cleft%287%20x%20-%206%5Cright%29%20%3D%20%5Cleft%287%20x%20-%206%5Cright%29%20%5Cleft%282%20x%5E%7B2%7D%20%2B%201%5Cright%29%20" alt="LaTeX:  \displaystyle 2 x^{2} \left(7 x - 6\right) +1 \cdot \left(7 x - 6\right) = \left(7 x - 6\right) \left(2 x^{2} + 1\right) " data-equation-content=" \displaystyle 2 x^{2} \left(7 x - 6\right) +1 \cdot \left(7 x - 6\right) = \left(7 x - 6\right) \left(2 x^{2} + 1\right) " /> . </p> </p>