Search 73,200 tutors
FIND TUTORS
Ask a question
0 0

what is m^3-3m^2=5m-15 factored?

Tutors, please sign in to answer this question.

3 Answers

What is m^3 – 3m^2 = 5m – 15 factored?
 
It's interesting that the problem was posed this way because you might notice that you can use the Distributive Property on both sides:
 
m^2(m – 3) = 5(m – 3)
 
At this point you might decide to say "If m ≠ 3 then I can divide both sides by (m–3) to get m^2 = 5, where m = ±√(5) are the only two answers."
 
However, if instead you subtracted 5(m – 3) from both sides:
 
m^2(m – 3) – 5(m – 3) = 0
 
and used the Distributive Property:
 
(m – 3)(m^2 – 5) = 0
 
Substitute (√(5))^2 for 5:
 
(m – 3)(m^2 – (√(5))^2) = 0
 
Use Difference of Squares:
 
(m – 3)(m + √(5))(m – √(5)) = 0
 
That's the answer to, "What is m^3 – 3m^2 = 5m – 15 factored?"
 
But now, using the Zero Product Property, you can find the values of m that make it true:
 
(m – 3) = 0 ==> m = 3
(m – √(5)) = 0 ==> m = + √(5)
(m + √(5)) = 0 ==> m = – √(5)
Hi Tabalina;
m^3-3m^2=5m-15
Let's bring everything to one side...
m3-3m2-5m+15=0
For the FOIL...
FIRST must be (m2)(m)=m3
(m2...)(m...)
OUTER must be (-3)(m2)=-3m2
(m2...)(m-3)
INNER must be (-5)(m)=-5m
(m2-5)(m-3)
LAST must be (-5)(-3)=15
0=(m2-5)(m-3)
Either or both parenthetical equation(s) must equal zero...
0=m2-5.........0=m-3
5=m2............3=m
+/- √5=m
Please remember that - √5, when squared, produces the same result as +√5, when squared.
There are three answers...
m=-√5, +√5 and 3
 
 
The first step is to reorganize the equation to get a zero on the right hand side
 
m3 - 3m2 - 5 m + 15  = 0
 
The cubic expression on the left hand side can be factored by a method called factoring by grouping.
This method does not always work, but is very good when it does.
 
Step 1:   pull a factor of m2 out of the first two terms   m2 (m -3)
Step 2:   pull a factor of -5 out of the last two terms     -5(m-3)
Step 3:   {this is the good part}  notice that in both  steps 1 and 2 we got a factor of (m-3)
Step 4:  take advantage of this good fortune to write the whole expression as (m-3) ( m2 -5)
           This ends the factor by grouping part
Step 5:   m2 -5   factors as  (m- sqrt(5) ) (m + sqrt(5))
 
Final answer (m-3) (m - sqrt(5)) ( m+ sqrt(5))  = 0
 
  So the solutions to the problem are
       m = 3
      m = - sqrt(5)
      m = + sqrt(5)
 
 

Seattle algebra 1 tutors