SOLUTION: A Polynomial Function for Volume The polynomial function given below represents the volume of a rectangular prism with a square base. Each binomial factor of the polynomial repr

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A Polynomial Function for Volume The polynomial function given below represents the volume of a rectangular prism with a square base. Each binomial factor of the polynomial repr      Log On


   

Question 1105249: A Polynomial Function for Volume
The polynomial function given below represents the volume of a rectangular prism with a square base. Each binomial factor of the polynomial represents one dimension of the rectangular prism.
f(x) = x^3 + x^2 – 21x – 45
Use the Remainder Theorem to determine whether the binomials x – 5 and x + 1 represent dimensions of the rectangular prism. Enter your answer and explanation in the box.
Rewrite the given function as a product of binomial factors. Enter your answer and explanation in the box.
The area of the base of the rectangular prism is 289 cm2. What are the dimensions of the rectangular prism? Enter your answer and explanation in the box.
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


(1) f%285%29+=+5%5E3%2B5%5E2-21%2A5-45+=+125%2B25-105-45+=+0
Yes, (x-5) is a factor of f(x), so (x-5) represents a dimension of the prism.

f%28-1%29+=+%28-1%29%5E3%2B%28-1%29%5E2-21%28-1%29-45+=+-1%2B1%2B21-45+=+-24
No, (x+1) is not a factor of f(x), so (x+1) does not represent a dimension of the prism.

(2) x%5E3%2Bx%5E2-21x-45+=+%28x-5%29%28x%5E2%2B6x%2B9%29+=+%28x-5%29%28x%2B3%29%5E2

(3) %28x%2B3%29%5E2+=+289
x%2B3+=+17
x+=+14

The dimensions are (x+3) by (x+3) by (x-5) = 17x17x9.