Chapter 8.5, Problem 60PPE

To determine

To calculate: The factor of $p^6+14p^3-72$

Answer to Problem 60PPE

  $(p^3-4)(p^3+18)$

Explanation of Solution

Given information: The expression $p^6+14p^3-72$

Calculation:

  $\begin{array}{l}{p}^6+14p^3-72\\ $ ={(p^3)}^2+14p^3-72$$ ={(p^3)}^2+(18-4)p^3-72[\because 72=18\times 4\text{and}\text{ 14}=18-4]$$ ={(p^3)}^2+18p^3-4p^3-72$$ =\{{(p^3)}^2+18p^3\}-\{4p^3+72\}$=p^3(p^3+18)-4(p^3+18)\\ =(p^3-4)(p^3+18)\end{array}$

Thus, $p^6+14p^3-72=(p^3-4)(p^3+18)$