Question

select the correct answer.
averages company operates two factories. their outputs are represented by these expressions, where b is the number of boxes produced.
factory a : 3b³ = 8b² + b - 130
factory b : 4b³ = 9b - 360
which polynomial represents the companys total output?
a. 3b³ + b³ - 2b - 360
b. 6b³ = 6b² + b + 360
c. 6b³ = 9b³ - 9b = 140
d. 9b³ = 7b² + 4b + 140

Explanation:

Step1: Add the two polynomials

$(2b^3 - 3b^2 + b - 120) + (4b^3 - 3b - 260)$

Step2: Combine like terms for $b^3$

$2b^3 + 4b^3 = 6b^3$

Step3: Combine like terms for $b^2$

$-3b^2 + 0b^2 = -3b^2$

Step4: Combine like terms for $b$

$b - 3b = -2b$

Step5: Combine constant terms

$-120 - 260 = -380$

Step6: Assemble the total polynomial

$6b^3 - 3b^2 - 2b - 380$

Answer:

C. $6b^3 - 3b^2 - 2b - 380$