The local Beep Boop store sells widgets and gizmos. If you subtract the cost of 3 gizmos from 7
widgets you would spend 28 Boop Bucks. Also,
you would spend 16 Boop Bucks if you bought 4
widgets and 2 gizmos. Which of the two items,
widgets or gizmos, does the Beep Boop store give
away for free? How do you know? How much
does the other item cost? Make sure you answer
in Boop Bucks.

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).