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

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Question 1105250: 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

g(x) is a fourth-degree polynomial function with the following properties.
�g(x) has the same real zeros as f(x).
�g(x) has at least one imaginary zero.
Find a possible equation for g(x). Write your equation in standard form. Enter your answer and explanation in the box.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39623) (Show Source):
You can put this solution on YOUR website!
Possible roots based on Rational Roots Theorem include -3, +3, -5, +5, and others.
Trying polynomial, OR synthetic division gives this factorization for f:

Since the description gives that the box has a square base, the side of each base dimension is the . Length is and width is .

The height of the box would be .

Answer by greenestamps(13203) (Show Source):
You can put this solution on YOUR website!

; its zeros are 5 and -3.

If g(x) is a polynomial of degree 4 with the same real zeros as f(x) and with at least one imaginary root, then it must have single real zeros of 5 and -3 and one pair of imaginary zeros.

With only those restrictions, a possible polynomial g(x) is