Answer:
V = x³ + 7x² + 15x + 9
Step-by-step explanation:
We are told that V = (1/3)Bh (volume is 1/3 the area of the base times the
height, here B is the area of the base, h
is the height)
We are given:
B = 3x² + 12x + 9
h = x + 3
So
V = (1/3)(3x² + 12x + 9)(x + 3)
Now multiply to simplify, we'll ignore the 1/3 for now
(3x² + 12x + 9)(x + 3) = 3x²(x) + 12x(x) + 9(x) + 3x²(3) + 12x(3) + 9(3)
which simplifies to
3x³ + 12x² + 9x + 9x² + 36x + 27
which simplifies to
3x³ + 21x² + 45x + 27
So V = (1/3)(3x³ + 21x² + 45x + 27)
Distribute the 1/3 to all terms and simlify
V = (1/3)3x³ + (1/3)21x² + (1/3)45x + (1/3)27
V = x³ + 7x² + 15x + 9
