Final answer:
The correct factored form of the polynomial x²+x−72 is (x+9)(x−8).
Step-by-step explanation:
The student is seeking to factor the quadratic polynomial x²+x−72. To factor this polynomial, we look for two numbers that multiply to −72 and add up to 1, which are the coefficients of the quadratic and linear terms, respectively.
After testing various pairs of factors of −72, we find that 9 and −8 satisfy these conditions because 9(−8) gives −72 and 9+(−8) gives 1. Therefore, the polynomial can be factored as (x+9)(x−8).