1. The problem asks for a pair of factors of -90 whose sum is -1. 2. We start by listing pairs of numbers that multiply to -90. 3. Because the product is negative, one number must be positive and the other negative. 4. Possible pairs: $(1,-90), (-1,90), (2,-45), (-2,45), (3,-30), (-3,30), (5,-18), (-5,18), (6,-15), (-6,15), (9,-10), (-9,10)$. 5. Now, we check the sums for each pair: - $1 + (-90) = -89$ - $-1 + 90 = 89$ - $2 + (-45) = -43$ - $-2 + 45 = 43$ - $3 + (-30) = -27$ - $-3 + 30 = 27$ - $5 + (-18) = -13$ - $-5 + 18 = 13$ - $6 + (-15) = -9$ - $-6 + 15 = 9$ - $9 + (-10) = -1$ - $-9 + 10 = 1$ 6. The pair whose sum is $-1$ is $9$ and $-10$. Answer: The factor pair is $\boxed{9 \text{ and } -10}$.