Final answer:
Sarah lost a total of 26 points in the game, represented by the integer -26.
Step-by-step explanation:
The question involves simple arithmetic operations for calculating the total change to Sarah's score in a game. First, we need to calculate the points Sarah lost by losing four points five times. This is done by multiplying 4 (the points lost each time) by 5 (the number of times she lost points), which equals 20 points lost. Next, we multiply 2 (the points lost) by 3 (the number of times she lost points again) for a total of 6 points lost. The total points Sarah lost in the game is the sum of these two amounts: 20 points + 6 points, which is 26 points lost. The total change to her score as an integer is therefore -26, as losing points is represented by a negative integer.