Matt received a quote to move his belongings to his new house. The estimate from the mover is $815 for 8 hours of packing and 7 hours of moving. Matt thinks he can reduce his cost by doing some of the packing and moving himself. If he does, the cost will decrease to $615 for 5 hours of packing and 6 hours of moving. If the mover charges a set hourly rate for packing and another set hourly rate for moving, what are these hourly rates?

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).