Questions: Complete the table by listing the pairs of factors of the number. and the sum of each pair. (Separate factors with a comma. Enter your answers in order from smallest to largest sum.)

Solution Steps

To solve this problem, we need to find all pairs of factors of -28 and then calculate the sum of each pair. We will list the pairs in order from the smallest to the largest sum.

1. Identify all pairs of factors of -28.
2. Calculate the sum of each pair.
3. Sort the pairs based on their sums in ascending order.

The factors of \(-28\) can be expressed as pairs. The complete list of factor pairs is: \[ (1, -28), (-1, 28), (2, -14), (-2, 14), (4, -7), (-4, 7), (7, -4), (-7, 4), (14, -2), (-14, 2), (28, -1), (-28, 1) \]

Next, we calculate the sum of each factor pair: \[ \begin{align_} (1, -28) & : 1 + (-28) = -27 \\ (-1, 28) & : -1 + 28 = 27 \\ (2, -14) & : 2 + (-14) = -12 \\ (-2, 14) & : -2 + 14 = 12 \\ (4, -7) & : 4 + (-7) = -3 \\ (-4, 7) & : -4 + 7 = 3 \\ (7, -4) & : 7 + (-4) = 3 \\ (-7, 4) & : -7 + 4 = -3 \\ (14, -2) & : 14 + (-2) = 12 \\ (-14, 2) & : -14 + 2 = -12 \\ (28, -1) & : 28 + (-1) = 27 \\ (-28, 1) & : -28 + 1 = -27 \\ \end{align_} \]

The pairs sorted by their sums in ascending order are: \[ \begin{align_} (1, -28) & : -27 \\ (-28, 1) & : -27 \\ (2, -14) & : -12 \\ (-14, 2) & : -12 \\ (4, -7) & : -3 \\ (-7, 4) & : -3 \\ (-4, 7) & : 3 \\ (7, -4) & : 3 \\ (-2, 14) & : 12 \\ (14, -2) & : 12 \\ (-1, 28) & : 27 \\ (28, -1) & : 27 \\ \end{align_} \]

Final Answer