Question

what is ((v - 3)(5v^2 + 3v + 5))?

a. (5v^3 - 11v^2 - 4v - 15)
b. (5v^3 - 12v^2 - 5v - 14)
c. (5v^3 - 12v^2 - 4v - 15)
d. (5v^3 - 12v^2 - 4v + 15)

Explanation:

Step1: Distribute $v$ to each term

$v(5v^2 + 3v + 5) = 5v^3 + 3v^2 + 5v$

Step2: Distribute $-3$ to each term

$-3(5v^2 + 3v + 5) = -15v^2 - 9v - 15$

Step3: Combine the two results

$5v^3 + 3v^2 + 5v - 15v^2 - 9v - 15$

Step4: Combine like terms

$5v^3 + (3v^2 - 15v^2) + (5v - 9v) - 15 = 5v^3 - 12v^2 - 4v - 15$

Answer:

c. $5v^3 - 12v^2 - 4v - 15$