Answer:
Possible expressions of length, width and height are 5x, (3x + 2) and (4x + 7)
Step-by-step explanation:
Since volume of the prism is represented by
V = Length × width × height
Expression that represents the volume of the rectangular prism has been given as 60x³ + 145x² + 70x
Now we will factorize this expression to convert it into the length, width and height form.
V = 60x³ + 145x² + 70x
= 5x(12x² + 29x + 14)
= 5x[ 12x² + 21x + 8x + 14]
= 5x[3x(4x + 7) + 2(4x + 7)]
= 5x[ (3x + 2)(4x + 7)]
= 5x (3x + 2)(4x + 7)
Now we can say that the possible expressions of length, width and height are 5x, (3x + 2) and (4x + 7)
