Respuesta :
Option C: [tex]5 x(4 x+7)(3 x+2)[/tex] is the possible expressions for length, width and height of the prism.
Explanation:
The volume of the rectangular prism is [tex]60 x^{3}+145 x^{2}+70 x[/tex]
To determine the length, width and height of the rectangular prism, let us factor the expression.
Thus, factoring 5x from the expression, we have,
[tex]5 x\left(12 x^{2}+29 x+14\right)[/tex]
Let us break the expression [tex]12 x^{2}+29 x+14[/tex] into two groups, we get,
[tex]5x[\left(12 x^{2}+8 x\right)+(21 x+14)][/tex]
Factoring 4x from the term [tex]12 x^{2}+8 x[/tex] , we get,
[tex]5x[4 x(3 x+2)+(21x+14)][/tex]
Similarly, factoring 7x from the term [tex]21 x+14[/tex] , we get,
[tex]5x[4 x(3 x+2)+7(3x+2)][/tex]
Now, let us factor out [tex]3x+2[/tex], we get,
[tex]5 x(4 x+7)(3 x+2)[/tex]
Hence, the possible expressions for length, width and height of the prism is [tex]5 x(4 x+7)(3 x+2)[/tex]
Therefore, Option C is the correct answer.
