for questions 1-2, simplify the rational expression. state any restrictions on the variable. p^2-4p-32/p+4
A. -p+8; p not equal-4
B. p-8; p not equal-4
C. -p-8; p not equal-4
D. p+8; p not equal-4
To simplify the rational expression (p^2-4p-32)/(p+4), we need to factor the numerator.
The numerator is a quadratic expression, so let's find two numbers that multiply to give -32 and add to give -4.
The numbers are -8 and 4, because -8 * 4 = -32 and -8 + 4 = -4.
So, we can rewrite the numerator as: (p-8)(p+4).
Now, we can simplify the expression (p^2-4p-32)/(p+4) to (p-8)(p+4)/(p+4).
Notice that the (p+4) in the numerator cancels out with the (p+4) in the denominator.
So, the simplified expression is p-8.
The restriction is p ≠ -4 because division by zero is undefined. Therefore, the correct answer is B. p-8; p not equal-4.