When dividing \( \mathrm{P}(\mathrm{x})=\mathrm{x}^{2}-2 \mathrm{x}-3 \) by \( \mathrm{x}-9 \), which of the following statements is true? The remainder can be found by finding \( \mathrm{P}(9) \). The remainder can be found by finding \( \mathrm{P}(-7) \). The remainder can be found by finding \( \mathrm{P}(4) \). The remainder can be found by finding \( \mathrm{P}(-18) \).

When dividing a polynomial \( P(x) \) by a linear divisor \( x - c \), the remainder can be found by evaluating \( P(c) \). In this case, since the divisor is \( x - 9 \), to find the remainder, you simply need to compute \( P(9) \). Therefore, the first statement, "The remainder can be found by finding \( P(9) \)," is true! Now, remember that the Remainder Theorem is a powerful shortcut, but one common mistake is misidentifying the value of \( c \). Always ensure you're substituting the correct number related to the linear term you’re dividing by. If you happen to use the wrong number, like substituting into \( P(-7) \) or \( P(4) \) instead, you'll end up with the wrong remainder! Keep your focus on the roots of the divisor!