Chapter 8.8, Problem 38PPE

To determine

To find:Total number of factors, in which given expression for volume will be factorized.

Answer to Problem 38PPE

Expression representing volume will have three factors. Also, first step in factoring is, taking greatest common factor from its all three terms.

Explanation of Solution

Giveninformation: Volume of the bat`s house is given by the expression, $V=4x^3+22x^2+24x$ .

Concept/Formula used:Bat`s house is in cuboidal form, so its volume will be given be the formula,

Volume of cuboid $=\text{ Height}\times \text{base}\times \text{width}$

So, find three factors of given expression to represent its volume as a product of its dimensions.

Calculation:In given expression, take $2x$ out as greatest common factor,

  $4x^3+22x^2+24x=2x(2x^2+11x+12)$

Its quadratic polynomial is further factorized as,

  $\begin{array}{l}V=2x(2x^2+(8+3)x+12)\\ =2x(2x^2+8x+3x+12)\\ =2x(2x(x+8)+3(x+8))\\ =2x(x+8)(2x+3)\end{array}$

Conclusion: Thus, expression representing volume, as its degree is 3, will have three factors as its three dimensions. And first step in factoring this expression representing volume is, taking greatest common factor from its all three terms.