Question

The volume of the rectangular prism is 60x3 + 145x2 + 70x. factor to find the possible expressions for length, width and height of the prism.

Answer 1

Possible expressions of length, width and height are 5x, (3x + 2) and (4x + 7)

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)

Answer 2

The possible dimensions of the prism will be evaluated as follows:
60x3 + 145x2 + 70x
factoring out
factoring out 5x we get:
5x(12x^2+29x+14)
factoring the quadratic we get:
5x(3x+2)(4x+7)
hence the dimensions are:
5x by (3x+2) by (4x+7)