Chapter 7.8, Problem 33E

To determine

To Identify: Error in factoring the given polynomial completely.

Answer to Problem 33E

  $-6$ must be factored out instead of $6$ .

Correct factorization is $a^3+8a^2-6a-48=a^2(a+8)-6(a+8)$

  $=(a+8)(a^2-6)$

Explanation of Solution

Given information:

Given incorrect factorization is $a^3+8a^2-6a-48=a^2(a+8)+6(a+8)$

  $=(a+8)(a^2+6)$

Calculation:

Instead of factoring out $6$ ; $-6$ must be factored out. Then,

  $a^3+8a^2-6a-48=a^2(a+8)-6(a+8)$

  $=(a+8)(a^2-6)$

Thus,

  $a^3+8a^2-6a-48=(a+8)(a^2-6)$ .