Question

1. \\(\frac{p^2 - 3p - 54}{p - 9}\\)

Explanation:

Step 1: Factor the numerator

We need to factor the quadratic expression \( p^2 - 3p - 54 \). We look for two numbers that multiply to \( -54 \) and add up to \( -3 \). The numbers are \( -9 \) and \( 6 \) because \( -9\times6=-54 \) and \( -9 + 6=-3 \). So, we can factor the numerator as:
\( p^2 - 3p - 54=(p - 9)(p + 6) \)

Step 2: Simplify the fraction

Now we have the fraction \( \frac{(p - 9)(p + 6)}{p - 9} \). Assuming \( p
eq9 \) (to avoid division by zero), we can cancel out the common factor \( p - 9 \) in the numerator and the denominator:
\( \frac{(p - 9)(p + 6)}{p - 9}=p + 6 \)

Answer:

\( p + 6 \) (for \( p
eq9 \))