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For questions 1-2, simplify the rational expression. State any restrictions on the variable. (p^(2)-4p-32)/(p+4)
For questions 1-2, simplify the rational expression. State any restrictions on the variable. (p^(2)-4p-32)/(p+4)
Final answer:The rational expression (p²-4p-32)/(p+4) simplifies to p-8 with a restriction that p cannot equal -4, to avoid making the denominator zero.Explanation:To simplify the rational expression (p²-4p-32)/(p+4), first, we factor the numerator. We are looking for factors of -32 that sum to -4, which are -8 and 4. Thus, the factorization of the numerator is (p-8)(p+4). The expression simplifies to:(p-8)(p+4) / (p+4) = p-8, as long as p ≠ -4The restriction on the variable p is that it cannot equal -4 because it would make the denominator zero, causing the expression to be undefined. Thus, our simplified expression is p - 8, with the restriction p ≠ -4....
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