Chapter 8.8, Problem 28P

Factor completely.

$28.32m^3+72m^2-80m-180$

To determine

The factors of given expression $32m^3+72m^2-80m-180$ .

Answer to Problem 28P

  $4\left(4m+9\right)\left(2m^2-5\right)$ .

Explanation of Solution

Given information:The expressionis $32m^3+72m^2-80m-180$ .

Calculation:

As per the given expression $32m^3+72m^2-80m-180$ , 4 is common in each term.

So, by taking 4 common from each term,

  $32m^3+72m^2-80m-180$

  $=4\left(8m^3+18m^2-20m-45\right)$

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

  $2m^2$ Is GCF in $8m^3+18m^2$ and -5 is the GCF in $-20m-45$

So, it can be further written as $4[2m^2\left(4m+9\right)-5\left(4m+9\right)]$ .

As we can see that $\left(4m+9\right)$ is a common factor in both the terms.

So, finally $32m^3+72m^2-80m-180$ = $4\left(4m+9\right)\left(2m^2-5\right)$

Conclusion: The factors of the given expression are $4\left(4m+9\right)\left(2m^2-5\right)$ .