Given the functions, f(x) = x 2 + x - 5 and g(x) = 4x 2 - 2x + 1, perform the indicated operation. when applicable, state the domain restriction.

(f - g)(x)

a) -3x2 - x - 4
b) -3x2 + 3x - 6
c) 3x2 - x - 4
d) 3x2 - x - 6

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).