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Completion requirements
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Determine the greatest common factor of \(22w^4u^3v \), \(11w^4u^2v \), and \(121w^3u^2v^2 \).
Expression Prime Factorization
\(22x^4u^3v \)
\(= 11 \cdot 2 \cdot w \cdot w \cdot w \cdot w \cdot u \cdot u \cdot u \cdot v \)
\(11w^4u^2v \)
\(= 11 \cdot w \cdot w \cdot w \cdot w \cdot u \cdot u \cdot v \) \(121w^3u^2v^2\) \(= 11 \cdot 11 \cdot w \cdot w \cdot w \cdot u \cdot u \cdot v \cdot v \)
GCF \(= 11 \cdot w \cdot w \cdot w \cdot u \cdot u \cdot v \)
\(= 11w^3u^2v\)
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Factor the following binomials:
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\(33x^2 - 3x \)
GCF = \(3x \)
\(\begin{align}
\frac{{33x^2 - 3x}}{{3x}} &= \frac{{33x^2 }}{{3x}} - \frac{{3x}}{{3x}} \\
&= 11x - 1 \\
33x^2 - 3x &= 3x\left( {11x - 1} \right) \\
\end{align}\)
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\(18t^2 - 36t \)
GCF = \(18t \)
\(\begin{align}
\frac{{18t^2 - 36t}}{{18t}} &= \frac{{18t^2 }}{{18t}} - \frac{{36t}}{{18t}} \\
&= t - 2 \\
18t^2 - 36t &= 18t\left( {t - 2} \right) \\
\end{align}\)