The work of a student to solve a set of equations is shown:
equation 1: m = 8 + 2n
equation 2: 3m = 4 + 4n
step 1:
−3(m) = −3(8 + 2n) [equation 1 is multiplied by −3.]
3m = 4 + 4n [equation 2]
step 2:
−3m = −24 − 6n [equation 1 in step 1 is simplified.]
3m = 4 + 4n [equation 2]
step 3:
−3m + 3m = −24 − 6n + 4n [equations in step 2 are added.]
step 4:
0 = −24 − 2n
step 5:
n = −12
in which step did the student first make an error?
step 4
step 3
step 2
step 1

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).