Question

Please help me i need the answer right now. The lesson is Rational Root Theorem.

Answer 1

Explanation:

1. The length is one more thrice it's width. The height is 4 more than it width. We can represent the

• x+4.(3x+1)(x)
• The volume is 720.
• Volume of Rectangular prism is LxWXH. So the volume is equal to the terms all multiplied. which is

`(3x + 1)(x + 4)`

`(3 {x}^(2) + 13x + 4)x = 720`

Multiply it by x.

`3 {x}^(3) + 13 {x}^(2) + 4x = 720`

`3{x}^(3) + 13 {x}^(2) + 4 x - 720`

The possible roots

The possible roots are plus or minus is1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, and 720. By a long list of substitution, 5 is a root. So this means that x=5. So the width has to be

`x = 5`

2. First. we apply the Rational Root Theorem so the possible roots are plus or minus 1,2,3,6.

Let check via synethic division to see which are roots.

Let try 1 and -1 first. If we plug 1 into the equation, we get

`1 - 2 - 5 + 6 = 0`

So 1 or (x-1) is a solution. Since it's a solution we can divide this into our original polynomial to get us a new polynomial that is more simplified. If we apply synthetic division, we get a new polynomial in

`{x}^(2) - x - 6`

We can then factor this into

`(x - 3)(x + 2)`

So our roots or factors is

`(x - 1)(x - 3)(x + 2)`