Question 623310
Except for the 4, your formula is exactly correct. The general formula for volume of this shape (rectangular prism) is:
V = l*w*h
You got the length and width right. But the height is just x, not 4x. So the volume of your tray is:
V(x)=x(12-2x)(8.5-2x)<br>
This is not a polynomial, however. So we need to multiply it out. Distributing the x we get:
{{{V(x)=(12x-2x^2)(8.5-2x)}}}
Now we use FOIL to multiply the rest:
{{{V(x)=12x*8.5 + 12x*(-2x) + (-2x^2)*8.5 + (-2x^2)*(-2x)}}}
Simplifying...
{{{V(x)=102x + (-24x^2) + (-17x^2) + 4x^3}}}
{{{V(x)=102x + (-41x^2) + 4x^3}}}
Normally we write polynomials in order from highest exponent to lowest:
{{{V(x)=4x^3 + (-41x^2) + 102x}}}