Answer:
The missing length is 2x+5
Step-by-step explanation:
Given equation of volume of cuboid is V= [tex]2x^{3} +17x^{2} +46x+40[/tex]
Figure show that
Length of cuboid is ?
Width of cuboid is (x+4)
Height of cuboid is (x+2)
The volume of cuboid is given by
V=Length x Width x Height
Let Length be (bx+a)
The volume of cuboid will be
[tex]V=(bx+a)(x+4)(x+2)[/tex]
[tex]V=(bx+a)[x^{2}+4x+2x+8 ][/tex]
[tex]V=bx[x^{2}+6x+8]+a[x^{2}+6x+8][/tex]
[tex]V=[bx^{3}+6bx^{2}+8bx]+[ax^{2}+6ax+8a][/tex]
[tex]V=[bx^{3}+(6b+a)x^{2}+(8b+6a)x+8a][/tex]
On comparing coefficient with given equation of volume
We get,
b=2 and 8a=40
Therefore, the value of a is 5 and b is 2
Thus, The missing length is bx+a=2x+5
