Question

Please Help ASAP. Algebra 2 Polynomial Functions:
Please convert and answer the following questions using the numbers provided.
Length: 6 inches
Width: 2 inches
Height: 8 inches
Volume: 96
1. Rewrite the formula using the variable x for the length. Substitute the value of the volume found in step 2 for V and express the width and height of the object in terms of x plus or minus a constant. For example, if the height measurement is 4 inches longer than the length, then the expression for the height will be (x + 4).
2. Simplify the equation and write it in standard form.
3. Find the solutions to this equation algebraically using the Fundamental Theorem of Algebra, the Rational Root Theorem, Descartes' Rule of Signs, and the Factor Theorem.
4. Substitute 0 for the function notation and, using graphing technology, graph the function.
Please and thank you!!!

Answer 1

ok so if length = x x = 6
width = x -4 as 6 - 4 = 2
height = x + 2 6 + 2 = 8

so the volume is

\[V = x \times (x -4) \times (x +2)\]

so if the volume is 96

\[96 = x^2 -2x^2 -8x\]


hope this helps.

Answer 2

oops a slight mistake it should be

\[96 = x^3 - 2x^2 - 8x\]

well thats a good start, and I know a zero exists at x = 6.

that should help.