5. The distance from Newtown to Oldtown on the highway is (6x2 + 2x – 2) miles. Using the back roads, the distance is (5x2 – 8x – 6) miles. How many miles shorter is the second route? (1 point)
11x2 + 10x – 8
–x2 – 6x + 4
x2 + 10x + 4
x2 – 6x – 8
To find the difference in distance, we need to subtract the distance on the back roads from the distance on the highway:
(6x^2 + 2x - 2) - (5x^2 - 8x - 6)
Simplifying, we get:
6x^2 + 2x - 2 - 5x^2 + 8x + 6
Combining like terms, we get:
x^2 + 10x + 4
Therefore, the second route is (x^2 + 10x + 4) miles shorter than the highway route. The answer is (c) x^2 + 10x + 4.