The binomial that represents the length of the fish tank is a factor of the polynomial because V(15) = 0
How to show that the binomial that represents the length of the fish tank is a factor of the polynomial?
From the question, we have
Volume:
V(x) = (2x - 30)(2x -20)(2x -60)
V(x) = 8x^3 - 440x^2 + 7200x - 36000
The length is also given as:
L = 2x - 30
Set the length to 0
So, we have:
2x - 30 = 0
Add 30 to both sides
2x = 30
Divide both sides by 2
x = 15
Substitute x = 15 in V(x) = 8x^3 - 440x^2 + 7200x - 36000
V(15) = 8 * 15^3 - 440 * 15^2 + 7200 * 15 - 36000
Evaluate the products
V(15) = 27000 - 99000 + 108000 - 36000
Evaluate the sum and the difference
V(15) = 0
Hence, the binomial that represents the length of the fish tank is a factor of the polynomial because V(15) = 0
Read more about remainder theorem at:
https://brainly.com/question/24202892
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