To factor the quadratic expression \( j^2 - 20j + 19 \), we look for two numbers that multiply to 19 (the constant term) and add to -20 (the coefficient of the \( j \) term).
The numbers that meet these criteria are -1 and -19, since:
\[ -1 \times -19 = 19 \] \[ -1 + (-19) = -20 \]
Thus, we can factor the expression as follows:
\[ j^2 - 20j + 19 = (j - 1)(j - 19) \]
So the factored form of \( j^2 - 20j + 19 \) is:
\[ (j - 1)(j - 19) \]