Question

A box is made by cutting out squares of side x from an 8 in by 12 in piece of cardboard. The polynomial function V(x) = (8 - 2x)(12 - 2x)(x) represents the volume of box for any size square x. Multiply this expression to find the standard form for this polynomial function.

Select one:
a. V(x) = 4x3 - 32x2 + 96x
b. V(x) = -4x3 + 96x
c. V(x) = -x3 - 96
d. V(x) = x3 - 32x2 + 96x

Answer 1

@hartnn

Answer 2

FOIL the first two terms, then multiply everything by x.

Answer 3

Ok im going to help you ok

Answer 4

???

Answer 5

so 96+-16x+-24x+4x^2

Answer 6

EXAMPLE
V = 144x - 52x^2 + 4x^3
dV/dx = 144 - 104x + 12x^2
To maximize volume, set the derivative to zero:
12x^2 - 104x + 144 = 0
x = (-(-104) +/- sqrt((-104)^2 - 4(12)(144))) / (2*12)
x = (104 +/- sqrt(10816 - 6912)) / 24
x = (104 +/- sqrt(3904)) / 24
x =~ 6.9 or 1.7
But x can't be more than 4, or the length of the box would be negative, so therefore:
Height: x =~ 1.7
Length: 8 - 2x =~ 4.54
Width: 18 - 2x =~ 14.54
V =~ 114.2

Answer 7

4x^3-40x^2+96x

Answer 8

Yup!

Answer 9

is that the answer?

Answer 10

That seems right, but it's not one of the answers...

Answer 11

ok thanks