For questions 1–2, simplify the rational expression. State any restrictions on the variable.
p squared minus four p minus thirty-two over p plus four
To simplify the rational expression (p^2 - 4p - 32)/(p + 4), we first factor the numerator:
p^2 - 4p - 32 = p^2 - 8p + 4p - 32
= p(p - 8) + 4(p - 8)
= (p + 4)(p - 8)
Now we rewrite the original expression with the factored numerator:
(p + 4)(p - 8)/(p + 4)
Next, we cancel out the common factor of (p + 4):
(p - 8)
Therefore, the simplified expression is (p - 8). There are no restrictions on the variable p since the original expression is defined for all real numbers.