Factorizetion \[ u^{2}+21^{u}+108 \]

To factor the quadratic expression \( u^{2} + 21u + 108 \), we look for two numbers that multiply to \( 108 \) and add up to \( 21 \). The numbers \( 9 \) and \( 12 \) fit these criteria because \( 9 + 12 = 21 \) and \( 9 \times 12 = 108 \). Thus, we can factor the expression as: \[ (u + 9)(u + 12). \] If you're solving this for any specific values, remember to set each factor equal to zero to find the roots of the equation. For example, \( u + 9 = 0 \) gives \( u = -9 \) and \( u + 12 = 0 \) gives \( u = -12 \). These solutions can help sketch the graph or understand its behavior!