Chapter 8.8, Problem 30P

Factor completely.

$96n^3-240n^2-168n+420$

To determine

Factorize the given expression $96n^3-240n^2-168n+420$

Answer to Problem 30P

  $12\left(4n^2-7\right)\left(2n-5\right)$

Explanation of Solution

Given information:

The expression is $96n^3-240n^2-168n+420$

Calculation:

As per the given expression $96n^3-240n^2-168n+420$ , 12 is common in each term.

So, by taking 12 common from each term,

  $96n^3-240n^2-168n+420=12\left(8n^3-20n^2-14n+35\right)$

Now, we find the greatest common factor (GCF) in each pair of the terms.

  $4n^2$ is the GCF in $8n^3-20n^2$ and $-7$ is the GCF in $-14n+35$

So, it can be further written as $12\left[4n^2\left(2n-5\right)-7\left(2n-5\right)\right]$

As we can see that $\left(2n-5\right)$ is a common factor in both the terms.

So, finally, $96n^3-240n^2-168n+420$

  $=12\left(2n-5\right)\left(4n^2-7\right)$

Conclusion: Therefore, the factors of given expression are $12\left(4n^2-7\right)\left(2n-5\right)$