1. 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 \(= 11 \cdot w \cdot w \cdot w \cdot u \cdot u \cdot v \)
    \(= 11w^3u^2v\)

  2. Factor the following binomials:

    1. \(33x^2 - 3x \)

      GCF = \(3x \)

      \(\begin{align}
       \frac{{33x^2 - 3x}}{{3x}} &= \frac{{33x^2 }}{{3x}} - \frac{{3x}}{{3x}} \\
        &= 11x - 1 \\
       33x^2 - 3x &= 3x\left( {11x - 1} \right) \\
       \end{align}\)

    2. \(18t^2 - 36t \)

      GCF = \(18t \)

      \(\begin{align}
       \frac{{18t^2 - 36t}}{{18t}} &= \frac{{18t^2 }}{{18t}} - \frac{{36t}}{{18t}} \\
        &= t - 2 \\
       18t^2 - 36t &= 18t\left( {t - 2} \right) \\
       \end{align}\)