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Questions: Algebra BusinessCalculus

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Algebra
Quadratics
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Factor \(\displaystyle 70 x^{3} - 50 x^{2} + 63 x - 45\).

Grouping the first two terms and factoring out their GCF, \(\displaystyle 10 x^{2}\), gives \(\displaystyle 10 x^{2}(7 x - 5)\). Grouping the last two terms and factoring out their GCF, \(\displaystyle 9\), gives \(\displaystyle 9(7 x - 5)\). The polynomial now has a common binomial factor of \(\displaystyle 7 x - 5\). This gives \(\displaystyle 10 x^{2} \left(7 x - 5\right) +9 \cdot \left(7 x - 5\right) = \left(7 x - 5\right) \left(10 x^{2} + 9\right)\).

Download \(\LaTeX\) 

\begin{question}Factor $70 x^{3} - 50 x^{2} + 63 x - 45$. 
    \soln{9cm}{Grouping the first two terms and factoring out their GCF, $10 x^{2}$, gives $10 x^{2}(7 x - 5)$. Grouping the last two terms and factoring out their GCF, $9$, gives $9(7 x - 5)$. The polynomial now has a common binomial factor of $7 x - 5$. This gives $10 x^{2} \left(7 x - 5\right) +9 \cdot \left(7 x - 5\right) = \left(7 x - 5\right) \left(10 x^{2} + 9\right)$. }

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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HTML for Canvas 
<p> <p>Factor  <img class="equation_image" title=" \displaystyle 70 x^{3} - 50 x^{2} + 63 x - 45 " src="/equation_images/%20%5Cdisplaystyle%2070%20x%5E%7B3%7D%20-%2050%20x%5E%7B2%7D%20%2B%2063%20x%20-%2045%20" alt="LaTeX:  \displaystyle 70 x^{3} - 50 x^{2} + 63 x - 45 " data-equation-content=" \displaystyle 70 x^{3} - 50 x^{2} + 63 x - 45 " /> . </p> </p>
HTML for Canvas
<p> <p>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}(7 x - 5) " src="/equation_images/%20%5Cdisplaystyle%2010%20x%5E%7B2%7D%287%20x%20-%205%29%20" alt="LaTeX:  \displaystyle 10 x^{2}(7 x - 5) " data-equation-content=" \displaystyle 10 x^{2}(7 x - 5) " /> . Grouping the last two terms and factoring out their GCF,  <img class="equation_image" title=" \displaystyle 9 " src="/equation_images/%20%5Cdisplaystyle%209%20" alt="LaTeX:  \displaystyle 9 " data-equation-content=" \displaystyle 9 " /> , gives  <img class="equation_image" title=" \displaystyle 9(7 x - 5) " src="/equation_images/%20%5Cdisplaystyle%209%287%20x%20-%205%29%20" alt="LaTeX:  \displaystyle 9(7 x - 5) " data-equation-content=" \displaystyle 9(7 x - 5) " /> . The polynomial now has a common binomial factor of  <img class="equation_image" title=" \displaystyle 7 x - 5 " src="/equation_images/%20%5Cdisplaystyle%207%20x%20-%205%20" alt="LaTeX:  \displaystyle 7 x - 5 " data-equation-content=" \displaystyle 7 x - 5 " /> . This gives  <img class="equation_image" title=" \displaystyle 10 x^{2} \left(7 x - 5\right) +9 \cdot \left(7 x - 5\right) = \left(7 x - 5\right) \left(10 x^{2} + 9\right) " src="/equation_images/%20%5Cdisplaystyle%2010%20x%5E%7B2%7D%20%5Cleft%287%20x%20-%205%5Cright%29%20%2B9%20%5Ccdot%20%5Cleft%287%20x%20-%205%5Cright%29%20%3D%20%5Cleft%287%20x%20-%205%5Cright%29%20%5Cleft%2810%20x%5E%7B2%7D%20%2B%209%5Cright%29%20" alt="LaTeX:  \displaystyle 10 x^{2} \left(7 x - 5\right) +9 \cdot \left(7 x - 5\right) = \left(7 x - 5\right) \left(10 x^{2} + 9\right) " data-equation-content=" \displaystyle 10 x^{2} \left(7 x - 5\right) +9 \cdot \left(7 x - 5\right) = \left(7 x - 5\right) \left(10 x^{2} + 9\right) " /> . </p> </p>