Fill in the missing work and justification for step 2 when solving 3(x + 2) = 12.

step work justification
1 3(x + 2) = 12 given
2
3 3x + 6 − 6 = 12 − 6 subtraction property of equality
4 3x = 6 simplify
5 three times x over three equals six over three division property of equality
6 x = 2 simplify

a. 3x + 6 = 12; distributive property

b. 3x + 2 = 12; distributive property

c. 3x + 6 = 12; multiplication property of equality

d. 3x + 2 = 12; multiplication property of equality

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).