Factoring!!!!!!!

Question

Ok, so the problem is:     9m³+18m²-25m-50

 

The answer is supposed to be (m+2)(3m+5)(3m-5)

 

How do I get to that? Please explain it to me!

Answer 1

Hi Taylor.

 

One approach to factoring cubic functions is grouping.

 

Your expression is

9m³+18m²-25m-50

 

If we group the terms, we have

(9m³+18m²) - (25m+50)

notice that the sign was changed from "-" to "+" before the last term because of the parentheses

 

Now let's try to factor each parenthetical term.

 

From the first parenthetical term, we can factor our a 9m²

(9m³+18m²) = 9m²(m+2)

and from the 2nd parenthetical term we can factor our a 25

(25m+50) = 25(m+2)

 

So putting this together we have

9m²(m+2) - 25(m+2)

 

Since both terms have a factor of (m+2), we have

(9m²-25)(m+2)

 

But notice that 9m²-25 is the difference between two squares and we can factor that term as follows:

(9m²-25) = (3m-5)(3m+5)

 

And (9m²-25)(m+2) = (3m-5)(3m+5)(m+2)