Chapter 8.7, Problem 34PPS

To determine

To find: The possible dimensions of prism whose volume is represented by given expression.

Answer to Problem 34PPS

The possible dimensions of prism are $2y$ , $\left(2y+5\right)$ , and $\left(2y+5\right)$ .

Explanation of Solution

Given information:

The volume of the prism is represented by the expression $8y^3+40y^2+50y$ . The dimensions are represented by polynomials with integer coefficients.

Concept used:

The factors of the expression representing the volume of prism are its dimensions.

Calculations:

The volume of the prism is represented by the expression $V=8y^3+40y^2+50y$ that can be written as

  $V=8y^3+40y^2+50y=2y\left(4y+20y+25\right)$

  $\Rightarrow V=2y\left(4y^2+20y+25\right)$

  $\Rightarrow V=2y\left(4y^2+20y+25\right)$

  $\Rightarrow V=2y\left({(2y)}^2+2\cdot 2y\cdot 5+{(5)}^2\right)$

  $\Rightarrow V=2y{\left(2y+5\right)}^2$

  $\Rightarrow V=2y\left(2y+5\right)\left(2y+5\right)$

Thus, the possible dimensions of prism are $2y$ , $\left(2y+5\right)$ , and $\left(2y+5\right)$ .

Conclusion:

The possible dimensions of prism are $2y$ , $\left(2y+5\right)$ , and $\left(2y+5\right)$ .