How do you factor 2m^2+ 11m + 5?

1 Answer
Apr 13, 2018

#m=-5,-1/2#

Explanation:

We know that one set of parentheses will be
#(2m+a)#

and the other will have to be
#(m+b)#

(Note: #a# and #b# are not the values from the equation, they are placeholders while solving)

So far we have:
#(2m+a)(m+b)=0#

Now let's find #a# and #b#

We know that #a*b=5*# because when you FOIL they have to multiply to equal #5#. Therefore, we know that one of them equals #5# and the other equals #1# because #5# is prime so those are its only factors.

We also know that #2m*b+a*m = 11m#. This can only be true if #b=5# and #a=1#. Now that we have found our values, let's solve for #m#.

#(2m+1)(m+5)=0#

Let's examine the first set of parentheses. We know that

#(2m+1)=0#

Subtract #1# from each side

#2m=-1#

Now divide each side by #2#

#m=-1/2#

Now, let's examine the second set of parentheses. We know that

#(m+5)=0#

Subtract #5# from each side

#m=-5#

Final answer:

#m=-5,-1/2#