A car is traveling along test track in the desert at a constant rate of 85 ft./s. The test track has a length of 10,000 feet, and the track is marked by foot for observation purposes. After eight seconds, the car is at foot marker 1000 feet. At what foot marker was the car at time Tegels zero seconds? Write a linear model for the location, L, of the car in the track as a function of time in seconds, T, that it has been traveling along the track. According to your model, will the car reach the end of the track in under two minutes? Justify

Evaluate 8x2 + 9x − 1 2x3 + 3x2 − 2x dx. solution since the degree of the numerator is less than the degree of the denominator, we don't need to divide. we factor the denominator as 2x3 + 3x2 − 2x = x(2x2 + 3x − 2) = x(2x − 1)(x + 2). since the denominator has three distinct linear factors, the partial fraction decomposition of the integrand has the form† 8x2 + 9x − 1 x(2x − 1)(x + 2) = correct: your answer is correct. to determine the values of a, b, and c, we multiply both sides of this equation by the product of the denominators, x(2x − 1)(x + 2), obtaining 8x2 + 9x − 1 = a correct: your answer is correct. (x + 2) + bx(x + 2) + cx(2x − 1).