Given:
The volume of the rectangular prism is
![V=4x^3+5x^2-32x-33](https://img.qammunity.org/2021/formulas/mathematics/high-school/zvl4wbwx93isyjw349mriacgvbcrs6e2j5.png)
Two dimensions are (x+1) and (x+3).
To find:
The missing dimension.
Solution:
We know that, volume of a rectangular prism is
![V=length* breadth* height](https://img.qammunity.org/2021/formulas/mathematics/high-school/vchi25euynd3o4e9kgp6pbuexi1u4iqsc8.png)
It means, volume of a rectangular prism is the product of all dimensions.
We have,
![V=4x^3+5x^2-32x-33](https://img.qammunity.org/2021/formulas/mathematics/high-school/zvl4wbwx93isyjw349mriacgvbcrs6e2j5.png)
Splitting the middle terms, we get
![V=4x^3+4x^2+x^2+x-33x-33](https://img.qammunity.org/2021/formulas/mathematics/high-school/ybphzfuaqeiwu1sm0mwn59xuq8038ryxt7.png)
![V=4x^2(x+1)+x(x+1)-33(x+1)](https://img.qammunity.org/2021/formulas/mathematics/high-school/5fy1wkoret42bbi2pvvprgu3jbryzl464a.png)
![V=(x+1)(4x^2+x-33)](https://img.qammunity.org/2021/formulas/mathematics/high-school/9ojd1f0jkr8jbxkclenaaviesrx4n4fa04.png)
Splitting the middle term, we get
![V=(x+1)(4x^2+12x-11x-33)](https://img.qammunity.org/2021/formulas/mathematics/high-school/ch5532ot5kg9k8je9k843za4atsiw3k8kv.png)
![V=(x+1)(4x(x+3)-11(x+3))](https://img.qammunity.org/2021/formulas/mathematics/high-school/enaaipveafp484tlqbnszjptbg6q2b2t0x.png)
![V=(x+1)(x+3)(4x-11)](https://img.qammunity.org/2021/formulas/mathematics/high-school/o7zqgponr3c8cx2ayeelzxmjqtv3ao3whl.png)
So, the three dimensions of the rectangular prism are (x+1), (x+3) and (4x-11).
Therefore, the missing dimension is (4x-11).