Answer:
height = x + 6
Explanation:
Volume = length x width x height
V = 10x³ + 67x² + 30x − 72
length = 5x - 4 and width = 2x + 3
So length x width = (5x - 4 ) x (2x + 3)
Using the FOIL method:
= (5x)(2x) + (5x)(3) + (-4)(2x) + (-4)(3)
= 10x² + 15x - 8x - 12
= 10x² + 7x -12
So to find height, divide Volume by (length x width)
10x³ + 67x² + 30x − 72 ÷ 10x² + 7x -12
Use polynomial long division. See image ( I did the best I could to capture the process)
The answer is x + 6
To verify
Multiply (5x-4) (2x + 3) (x + 6) = 10x³ + 67x² + 30x − 72