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Questions: Algebra BusinessCalculus

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Factor \(\displaystyle 40 x^{3} - 12 x^{2} + 10 x - 3\).

Grouping the first two terms and factoring out their GCF, \(\displaystyle 4 x^{2}\), gives \(\displaystyle 4 x^{2}(10 x - 3)\). Grouping the last two terms and factoring out their GCF, \(\displaystyle 1\), gives \(\displaystyle 1(10 x - 3)\). The polynomial now has a common binomial factor of \(\displaystyle 10 x - 3\). This gives \(\displaystyle 4 x^{2} \left(10 x - 3\right) +1 \cdot \left(10 x - 3\right) = \left(10 x - 3\right) \left(4 x^{2} + 1\right)\).

Download \(\LaTeX\) 

\begin{question}Factor $40 x^{3} - 12 x^{2} + 10 x - 3$. 
    \soln{9cm}{Grouping the first two terms and factoring out their GCF, $4 x^{2}$, gives $4 x^{2}(10 x - 3)$. Grouping the last two terms and factoring out their GCF, $1$, gives $1(10 x - 3)$. The polynomial now has a common binomial factor of $10 x - 3$. This gives $4 x^{2} \left(10 x - 3\right) +1 \cdot \left(10 x - 3\right) = \left(10 x - 3\right) \left(4 x^{2} + 1\right)$. }

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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HTML for Canvas 
<p> <p>Factor  <img class="equation_image" title=" \displaystyle 40 x^{3} - 12 x^{2} + 10 x - 3 " src="/equation_images/%20%5Cdisplaystyle%2040%20x%5E%7B3%7D%20-%2012%20x%5E%7B2%7D%20%2B%2010%20x%20-%203%20" alt="LaTeX:  \displaystyle 40 x^{3} - 12 x^{2} + 10 x - 3 " data-equation-content=" \displaystyle 40 x^{3} - 12 x^{2} + 10 x - 3 " /> . </p> </p>
HTML for Canvas
<p> <p>Grouping the first two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle 4 x^{2} " src="/equation_images/%20%5Cdisplaystyle%204%20x%5E%7B2%7D%20" alt="LaTeX:  \displaystyle 4 x^{2} " data-equation-content=" \displaystyle 4 x^{2} " /> , gives  <img class="equation_image" title=" \displaystyle 4 x^{2}(10 x - 3) " src="/equation_images/%20%5Cdisplaystyle%204%20x%5E%7B2%7D%2810%20x%20-%203%29%20" alt="LaTeX:  \displaystyle 4 x^{2}(10 x - 3) " data-equation-content=" \displaystyle 4 x^{2}(10 x - 3) " /> . 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(10 x - 3) " src="/equation_images/%20%5Cdisplaystyle%201%2810%20x%20-%203%29%20" alt="LaTeX:  \displaystyle 1(10 x - 3) " data-equation-content=" \displaystyle 1(10 x - 3) " /> . The polynomial now has a common binomial factor of  <img class="equation_image" title=" \displaystyle 10 x - 3 " src="/equation_images/%20%5Cdisplaystyle%2010%20x%20-%203%20" alt="LaTeX:  \displaystyle 10 x - 3 " data-equation-content=" \displaystyle 10 x - 3 " /> . This gives  <img class="equation_image" title=" \displaystyle 4 x^{2} \left(10 x - 3\right) +1 \cdot \left(10 x - 3\right) = \left(10 x - 3\right) \left(4 x^{2} + 1\right) " src="/equation_images/%20%5Cdisplaystyle%204%20x%5E%7B2%7D%20%5Cleft%2810%20x%20-%203%5Cright%29%20%2B1%20%5Ccdot%20%5Cleft%2810%20x%20-%203%5Cright%29%20%3D%20%5Cleft%2810%20x%20-%203%5Cright%29%20%5Cleft%284%20x%5E%7B2%7D%20%2B%201%5Cright%29%20" alt="LaTeX:  \displaystyle 4 x^{2} \left(10 x - 3\right) +1 \cdot \left(10 x - 3\right) = \left(10 x - 3\right) \left(4 x^{2} + 1\right) " data-equation-content=" \displaystyle 4 x^{2} \left(10 x - 3\right) +1 \cdot \left(10 x - 3\right) = \left(10 x - 3\right) \left(4 x^{2} + 1\right) " /> . </p> </p>